Friday, October 19, 2018

Number of the day: 1925

Properties of the number 1925:

1925 = 52 × 7 × 11 is the 1631th composite number and is not squarefree.
1925 has 3 distinct prime factors, 12 divisors, 13 antidivisors and 1200 totatives.
1925 has an emirp digit sum 17 in base 10.
1925 has an oblong digit product 90 in base 10.
Reversing the decimal digits of 1925 results in a sphenic number.
1925 = 53 + … + 93 is the sum of at least 2 consecutive cubes.
1925 = 9632 - 9622 = 1952 - 1902 = 1412 - 1342 = 932 - 822 = 512 - 262 = 452 - 102 is the difference of 2 nonnegative squares in 6 ways.
1925 is the difference of 2 positive pentagonal numbers in 5 ways.
1925 = 122 + 252 + 342 is the sum of 3 positive squares.
19252 = 11552 + 15402 = 5392 + 18482 is the sum of 2 positive squares in 2 ways.
19252 is the sum of 3 positive squares.
1925 is a proper divisor of 434 - 1.
1925 = '1' + '925' is the concatenation of 2 pentagonal numbers.
1925 is palindromic in (at least) the following bases: 37, 54, 76, -19, -20, -52, and -74.
1925 in base 15 = 885 and consists of only the digits '5' and '8'.
1925 in base 19 = 566 and consists of only the digits '5' and '6'.
1925 in base 36 = 1hh and consists of only the digits '1' and 'h'.
1925 in base 37 = 1F1 and consists of only the digits '1' and 'F'.
1925 in base 43 = 11X and consists of only the digits '1' and 'X'.

The number 1925 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000914: Stirling numbers of the first kind: s(n+2, n).
A001082: Generalized octagonal numbers: k*(3*k-2), k=0, +- 1, +- 2, +-3, ...
A002412: Hexagonal pyramidal numbers, or greengrocer's numbers.
A002623: G.f.: 1/((1-x)^4*(1+x)).
A029470: Numbers n such that n divides the (right) concatenation of all numbers <= n written in base 25 (most significant digit on left).
A033282: Triangle read by rows: T(n, k) is the number of diagonal dissections of a convex n-gon into k+1 regions.
A045944: Rhombic matchstick numbers: a(n) = n*(3*n+2).
A086810: Triangle obtained by adding a leading diagonal 1,0,0,0,... to A033282.
A115067: a(n) = (3*n^2 - n - 2)/2.
A303303: Generalized 23-gonal (or icositrigonal) numbers: m*(21*m - 19)/2 with m = 0, +1, -1, +2, -2, +3, -3, ...

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