852
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Number
$852$ (eight hundred and fifty-two) is:
- $2^2 \times 3 \times 71$
- The $24$th pentagonal number after $1$, $5$, $12$, $22$, $35$, $\ldots$, $477$, $532$, $590$, $651$, $715$, $782$:
- $852 = \ds \sum_{k \mathop = 1}^{24} \left({3 k - 2}\right) = \dfrac {24 \paren {3 \times 24 - 1} } 2$
- The $47$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $392$, $425$, $442$, $477$, $495$, $532$, $551$, $590$, $610$, $651$, $672$, $715$, $737$, $782$, $805$:
- $852 = \ds \sum_{k \mathop = 1}^{24} \left({3 k - 2}\right) = \dfrac {24 \paren {3 \times 24 - 1} } 2$
- The $42$nd Smith number after $4$, $22$, $27$, $58$, $\ldots$, $648$, $654$, $663$, $666$, $690$, $706$, $728$, $729$, $762$, $778$, $825$:
- $8 + 5 + 2 = 2 + 2 + 3 + 7 + 1 = 15$