651

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Number

$651$ (six hundred and fifty-one) is:

$3 \times 7 \times 31$

The $2$nd positive integer after $353$ such that its fourth power is the sum of $4$ other fourth powers of positive integers with no common factors:

$651^4 = 240^4 + 340^4 + 430^4 + 599^4$

The magic constant of a magic cube of order $6$, after $1$, $(9)$, $42$, $130$, $315$:

$651 = \ds \dfrac 1 {6^2} \sum_{k \mathop = 1}^{6^3} k = \dfrac {6 \paren {6^3 + 1} } 2$

The $21$st pentagonal number after $1$, $5$, $12$, $22$, $35$, $51$, $70$, $92$, $117$, $145$, $176$, $210$, $247$, $287$, $330$, $330$, $376$, $425$, $477$, $532$, $590$:

$651 = \ds \sum_{k \mathop = 1}^{21} \paren {3 k - 2} = \dfrac {21 \paren {3 \times 21 - 1} } 2$

The $31$st number whose divisor sum is square:

$\map {\sigma_1} {651} = 1024 = 32^2$

The $41$st generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $392$, $425$, $442$, $477$, $495$, $532$, $551$, $590$, $610$:

$651 = \ds \sum_{k \mathop = 1}^{21} \paren {3 k - 2} = \dfrac {21 \paren {3 \times 21 - 1} } 2$

The product with its reversal equals the product of another $3$-digit number with its reversal:

$651 \times 156 = 372 \times 273$

Arithmetic Functions on $651$

\(\ds \map {\sigma_1} { 651 }\)

\(=\)

\(\ds 1024\)

$\sigma_1$ of $651$

Also see

• Previous  ... Next: Magic Constant of Magic Cube
• Previous  ... Next: Fourth Powers which are Sum of 4 Fourth Powers
• Previous: Numbers whose Product with Reverse are Equal
• Previous  ... Next: Pentagonal Number
• Previous  ... Next: Generalized Pentagonal Number
• Previous  ... Next: Numbers whose Divisor Sum is Square

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $651$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $651$