66
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Number
$66$ (sixty-six) is:
- $2 \times 3 \times 11$
- The $2$nd after $55$ of the $3$ repdigit numbers which are also triangular
- The $3$rd sphenic number after $30$, $42$:
- $66 = 2 \times 3 \times 11$
- The $3$rd hexamorphic number after $1$, $45$:
- $66 = H_6$
- The $4$th number after $1$, $3$, $22$ whose divisor sum is square:
-
- $\map {\sigma_1} {66} = 144 = 12^2$
- The $5$th palindromic triangular number after $0$, $1$, $3$, $6$ whose index is itself palindromic:
- $66 = T_{11}$
- The $6$th hexagonal number after $1$, $6$, $15$, $28$, $45$:
- $66 = 1 + 5 + 9 + 13 + 17 + 21 = 6 \paren {2 \times 6 - 1}$
- The $6$th palindromic triangular number after $0$, $1$, $3$, $6$, $55$
- $66 = \dfrac {11 \times \paren {11 + 1} } 2$
- The $2$nd of those after $55$ which can be split into two palindromic halves
- The $11$th triangular number after $1$, $3$, $6$, $10$, $15$, $21$, $28$, $36$, $45$, $55$:
- $66 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 = \dfrac {11 \times \paren {11 + 1} } 2$
- The $15$th semiperfect number after $6$, $12$, $18$, $20$, $24$, $28$, $30$, $36$, $40$, $42$, $48$, $54$, $56$, $60$:
- $66 = 11 + 22 + 33$
- The $25$th of $35$ integers less than $91$ to which $91$ itself is a Fermat pseudoprime:
- $3$, $4$, $9$, $10$, $12$, $16$, $17$, $22$, $23$, $25$, $27$, $29$, $30$, $36$, $38$, $40$, $43$, $48$, $51$, $53$, $55$, $61$, $62$, $64$, $66$, $\ldots$
- The $38$th positive integer after $2$, $3$, $4$, $7$, $8$, $\ldots$, $50$, $54$, $55$, $59$, $60$, $61$, $65$ which cannot be expressed as the sum of distinct pentagonal numbers
- The $40$th (strictly) positive integer after $1$, $2$, $3$, $\ldots$, $37$, $38$, $42$, $43$, $44$, $48$, $49$, $50$, $54$, $55$, $60$, $61$, $65$ which cannot be expressed as the sum of distinct primes of the form $6 n - 1$
Also see
- Previous ... Next: Sphenic Number
- Previous ... Next: Hexagonal Number
- Previous ... Next: Hexamorphic Number
- Previous ... Next: Triangular Number
- Previous ... Next: Palindromic Triangular Numbers
- Previous ... Next: Repdigit Triangular Numbers
- Previous ... Next: Palindromic Triangular Numbers with Palindromic Halves
- Previous ... Next: Numbers not Expressible as Sum of Distinct Pentagonal Numbers
- Previous ... Next: Integers not Expressible as Sum of Distinct Primes of form 6n-1
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $66$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $66$