# 145

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## Number

$145$ (one hundred and forty-five) is:

$5 \times 29$

The $1$st term of the $3$rd $5$-tuple of consecutive integers have the property that they are not values of the $\sigma$ function $\map \sigma n$ for any $n$:
$\tuple {145, 146, 147, 148, 149}$

The $3$rd factorion base $10$ after $1$, $2$:
$145 = 1! + 4! + 5!$

The $6$th positive integer after $50$, $65$, $85$, $125$, $130$ which can be expressed as the sum of two square numbers in two or more different ways:
$145 = 12^2 + 1^2 = 9^2 + 8^2$

The $10$th pentagonal number after $1$, $5$, $12$, $22$, $35$, $51$, $70$, $92$, $117$:
$145 = 1 + 4 + 7 + 10 + 13 + 16 + 19 + 22 + 25 + 28 = \dfrac {10 \paren {3 \times 10 - 1} } 2$

The $14$th positive integer $n$ after $0$, $1$, $5$, $25$, $29$, $41$, $49$, $61$, $65$, $85$, $89$, $101$, $125$ such that the Fibonacci number $F_n$ ends in $n$

The $19$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $22$, $26$, $35$, $40$, $51$, $57$, $70$, $77$, $92$, $100$, $117$, $126$:
$145 = \dfrac {10 \paren {3 \times 10 - 1} } 2$