A353000 Quotients obtained when sigma(k) divides antisigma(k) with k = A076617(n), sigma (A000203) is the sum of divisors function and antisigma (A024816) is the sum of the non-divisors of n less than n function.

0, 0, 4, 4, 4, 37, 25, 68, 49, 122, 115, 340, 544, 487, 959, 2167, 1926, 4837, 3847, 6757, 6452, 3620, 11353, 13934, 9371, 16353, 9211, 30949, 49702, 17330, 32575, 72544, 62348, 109769, 145892, 51270, 173914, 130687, 61665, 102887, 351770, 446927, 504949, 258079

Offset

1,3

Comments

Note that the quotient obtained when sigma(k) divides k*(k+1)/2 with k = A076617(n) is a(n) + 1.

Links

Table of n, a(n) for n=1..44.

Formula

a(n) = A024816(A076617(n)) / A000203(A076617(n)).

Example

A076617(6) = 95; sigma(95) = 120 and antisigma(95) = 4440, hence a(6) = 4440 / 120 = 37.

Mathematica

Select[Table[(k*(k + 1)/2)/DivisorSigma[1, k] - 1, {k, 1, 10^6}], IntegerQ] (* Amiram Eldar, Apr 14 2022 *)

Prog

(PARI) is(n) = n*(n+1)/2%sigma(n) == 0; \\ A076617
f(n) = n*(n+1)/(2*sigma(n)) - 1;
lista(nn) = apply(f, select(is, [1..nn])); \\ Michel Marcus, Apr 15 2022

Crossrefs

Cf. A000203, A024816, A076617, A352810, A352811.

Sequence in context: A059812 A077725 A217940 * A372020 A182065 A325487

Adjacent sequences: A352997 A352998 A352999 * A353001 A353002 A353003

Keyword

nonn

Author

Bernard Schott, Apr 14 2022

Extensions

More terms from Amiram Eldar, Apr 14 2022

Status

approved