A392465 Sum of decimal digits of A101686.

1, 2, 1, 1, 8, 10, 19, 23, 19, 28, 29, 46, 55, 62, 64, 100, 77, 109, 109, 119, 127, 181, 143, 136, 172, 140, 199, 172, 236, 244, 253, 251, 226, 262, 266, 253, 325, 362, 307, 334, 341, 343, 388, 401, 361, 451, 434, 469, 451, 467, 433, 550, 518, 514, 487, 506

Offset

0,2

Comments

Let s_b(n) denote the sum of digits of a positive integer n when written in integer base b. It follows from Theorem 1.1 in Cilleruelo link that for any base b>=2, s_b(A101686(n)) > 2*log(n)/(30*log(b)) holds on a set of positive integers n of asymptotic density 1.

Links

Shreyansh Jaiswal, Table of n, a(n) for n = 0..1000

Javier Cilleruelo, Florian Luca, Juanjo Rué, and Ana Zumalacárregui, On the sum of digits of some sequences of integers, Open Mathematics, Vol. 11, No. 1 (2013), pp. 188-195.

Formula

a(n) = A007953(A101686(n)).

Example

a(5) = 10 because A101686(5) = 44200, and 4 + 4 + 2 = 10.

Mathematica

a[n_] := DigitSum[Abs[Pochhammer[1 + I, n]]^2]; Array[a, 56, 0] (* Amiram Eldar, Mar 24 2026 *)

Prog

(Python)
from math import prod
def A007953(n): return sum(int(d) for d in str(n)) # from A007953
def A101686(n): return prod(i**2+1 for i in range(1, n+1)) # from A101686
def a(n): return A007953(A101686(n))

Crossrefs

Cf. A007953, A101686.

Sequence in context: A156901 A167400 A225848 * A165889 A087127 A144946

Adjacent sequences: A392462 A392463 A392464 * A392466 A392467 A392468

Keyword

nonn,base

Author

Shreyansh Jaiswal, Mar 24 2026

Status

approved