26

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Number

$26$ (twenty-six) is:

$2 \times 13$

The $1$st non-palindromic integer whose square is palindromic:

$26^2 = 676$

The $2$nd nontotient after $14$:

$\nexists m \in \Z_{>0}: \map \phi m = 26$

where $\map \phi m$ denotes the Euler $\phi$ function

The $2$nd noncototient after $10$:

$\nexists m \in \Z_{>0}: m - \map \phi m = 26$

where $\map \phi m$ denotes the Euler $\phi$ function

The $3$rd heptagonal pyramidal number after $1$, $8$:

$26 = 1 + 7 + 18 = \dfrac {3 \paren {3 + 1} \paren {5 \times 3 - 2} } 6$

The $3$rd positive integer after $1$, $24$ whose Euler $\phi$ value is equal to the product of its digits:

$\map \phi {26} = 12 = 2 \times 6$

The $4$th second pentagonal number after $2$, $7$, $15$:

$26 = \dfrac {4 \paren {3 \times 4 + 1} } 2$

The $6$th Dudeney number after $0$, $1$, $8$, $17$, $18$:

$26^3 = 17 \, 576$, while $1 + 7 + 5 + 7 + 6 = 26$

The $8$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $22$:

$26 = \dfrac {4 \paren {3 \times 4 + 1} } 2$

The $10$th semiprime after $4$, $6$, $9$, $10$, $14$, $15$, $21$, $22$, $25$:

$26 = 2 \times 13$

The $11$th Ulam number after $1$, $2$, $3$, $4$, $6$, $8$, $11$, $13$, $16$, $18$:

$26 = 8 + 18$

The $11$th even number after $2$, $4$, $6$, $8$, $10$, $12$, $14$, $16$, $20$, $22$ which cannot be expressed as the sum of $2$ composite odd numbers.

The $17$th positive integer after $2$, $3$, $4$, $7$, $8$, $9$, $10$, $11$, $14$, $15$, $16$, $19$, $20$, $21$, $24$, $25$ which cannot be expressed as the sum of distinct pentagonal numbers.

The $20$th (strictly) positive integer after $1$, $2$, $3$, $\ldots$, $20$, $21$, $24$, $25$ which cannot be expressed as the sum of distinct primes of the form $6 n - 1$

Cannot be represented by the sum of less than $6$ hexagonal numbers:

$26 = 6 + 6 + 6 + 6 + 1 + 1$