Sunday, April 18, 2021

Number of the day: 651

Properties of the number 651:

651 = 3 × 7 × 31 is a sphenic number and squarefree.
651 has 3 distinct prime factors, 8 divisors, 7 antidivisors and 360 totatives.
651 has an oblong digit sum 12 in base 10.
651 has a sphenic digit product 30 in base 10.
651 has an oblong digit product 30 in base 10.
Reversing the decimal digits of 651 results in an oblong number.
651 = (10 × 11)/2 + … + (16 × 17)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
651 = 3262 - 3252 = 1102 - 1072 = 502 - 432 = 262 - 52 is the difference of 2 nonnegative squares in 4 ways.
651 is the sum of 2 positive triangular numbers.
651 is the difference of 2 positive pentagonal numbers in 1 way.
651 is the difference of 2 positive pentagonal pyramidal numbers in 1 way.
651 = (21 × (3 × 21-1))/2 is a pentagonal number.
651 = 12 + 52 + 252 is the sum of 3 positive squares.
6512 is the sum of 3 positive squares.
651 is a proper divisor of 4332 - 1.
651 = '6' + '51' is the concatenation of 2 semiprime numbers.
651 is palindromic in (at least) the following bases: 5, 6, 25, 30, 92, -4, -5, -26, -50, and -65.
651 in base 5 = 10101 and consists of only the digits '0' and '1'.
651 in base 6 = 3003 and consists of only the digits '0' and '3'.
651 in base 24 = 133 and consists of only the digits '1' and '3'.
651 in base 25 = 111 and consists of only the digit '1'.

The number 651 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000326: Pentagonal numbers: a(n) = n*(3*n-1)/2.
A001106: 9-gonal (or enneagonal or nonagonal) numbers: a(n) = n*(7*n-5)/2.
A001157: sigma_2(n): sum of squares of divisors of n.
A001318: Generalized pentagonal numbers: m*(3*m - 1)/2, m = 0, +-1, +-2, +-3, ....
A002061: Central polygonal numbers: a(n) = n^2 - n + 1.
A005728: Number of fractions in Farey series of order n.
A006095: Gaussian binomial coefficient [n,2] for q=2.
A022166: Triangle of Gaussian binomial coefficients (or q-binomial coefficients) [n,k] for q = 2.
A027441: a(n) = (n^4 + n)/2, (Row sums of an n X n X n magic cube, when it exists).
A139250: Toothpick sequence (see Comments lines for definition).

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