64

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Number

$64$ (sixty-four) is:

$2^6$

Represented as $100$ in octal and $1 \, 000 \, 000$ in binary.

The $1$st positive integer with $6$ or more prime factors:

$64 = 2 \times 2 \times 2 \times 2 \times 2 \times 2$

The $4$th of the $1$st ordered quadruple of consecutive integers that have divisor sums which are strictly increasing:

$\map {\sigma_1} {61} = 62$, $\map {\sigma_1} {62} = 96$, $\map {\sigma_1} {63} = 104$, $\map {\sigma_1} {64} = 127$

The $2$nd $6$th power after $1$:

$64 = 2 \times 2 \times 2 \times 2 \times 2 \times 2$

The $2$nd power of $8$ after $(1)$, $8$:

$64 = 8^2$

The $2$nd element of the $3$rd pair of integers $m$ whose values of $m \map {\sigma_0} m$ is equal:

$56 \times \map {\sigma_0} {56} = 448 = 64 \times \map {\sigma_0} {64}$

The $3$rd power of $4$ after $(1)$, $4$, $16$:

$64 = 4^3$

The $4$th cube number after $1$, $8$, $27$:

$64 = 4 \times 4 \times 4$

The total number of permutations of $r$ objects from a set of $4$ objects, where $1 \le r \le 4$

The $6$th power of $2$ after $(1)$, $2$, $4$, $8$, $16$, $32$:

$64 = 2^6$

The $6$th positive integer which cannot be expressed as the sum of a square and a prime:

$1$, $10$, $25$, $34$, $58$, $64$, $\ldots$

The $7$th almost perfect number after $1$, $2$, $4$, $8$, $16$, $32$:

$\map {\sigma_1} {64} = 127 = 2 \times 64 - 1$

The $8$th square number after $1$, $4$, $9$, $16$, $25$, $36$, $49$:

$64 = 8 \times 8$

The $8$th square after $1$, $4$, $9$, $16$, $25$, $36$, $49$ which has no more than $2$ distinct digits and does not end in $0$:

$64 = 8^2$

The $11$th powerful number after $1$, $4$, $8$, $9$, $16$, $25$, $27$, $32$, $36$, $49$

The $24$th of $35$ integers less than $91$ to which $91$ itself is a Fermat pseudoprime:

$3$, $4$, $9$, $10$, $12$, $16$, $17$, $22$, $23$, $25$, $27$, $29$, $30$, $36$, $38$, $40$, $43$, $48$, $51$, $53$, $55$, $61$, $62$, $64$, $\ldots$

Also see

• Previous  ... Next: Sequence of Powers of 8

• Previous  ... Next: Count of All Permutations on n Objects

• Previous  ... Next: Sequence of Powers of 4

• Previous  ... Next: Cube Number

• Previous  ... Next: Almost Perfect Number
• Previous  ... Next: Sequence of Powers of 2

• Previous  ... Next: Powerful Number
• Previous  ... Next: Squares with No More than 2 Distinct Digits
• Previous  ... Next: Square Number

• Previous: Pairs of Integers whose Product with Divisor Count are Equal

• Previous  ... Next: Numbers not Sum of Square and Prime

• Previous  ... Next: 91 is Pseudoprime to 35 Bases less than 91

• Previous  ... Next: Sequences of 4 Consecutive Integers with Rising Divisor Sum

• Next: Numbers with 6 or more Prime Factors

• Next: Sixth Power

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $64$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $64$