cp's OEIS Frontend

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.

%I A353000 #25 Apr 15 2022 10:01:30
%S A353000 0,0,4,4,4,37,25,68,49,122,115,340,544,487,959,2167,1926,4837,3847,
%T A353000 6757,6452,3620,11353,13934,9371,16353,9211,30949,49702,17330,32575,
%U A353000 72544,62348,109769,145892,51270,173914,130687,61665,102887,351770,446927,504949,258079
%N 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.
%C A353000 Note that the quotient obtained when sigma(k) divides k*(k+1)/2 with k = A076617(n) is a(n) + 1.
%F A353000 a(n) = A024816(A076617(n)) / A000203(A076617(n)).
%e A353000 A076617(6) = 95; sigma(95) = 120 and antisigma(95) = 4440, hence a(6) = 4440 / 120 = 37.
%t A353000 Select[Table[(k*(k + 1)/2)/DivisorSigma[1, k] - 1, {k, 1, 10^6}], IntegerQ] (* _Amiram Eldar_, Apr 14 2022 *)
%o A353000 (PARI) is(n) = n*(n+1)/2%sigma(n) == 0; \\ A076617
%o A353000 f(n) = n*(n+1)/(2*sigma(n)) - 1;
%o A353000 lista(nn) = apply(f, select(is, [1..nn])); \\ _Michel Marcus_, Apr 15 2022
%Y A353000 Cf. A000203, A024816, A076617, A352810, A352811.
%K A353000 nonn
%O A353000 1,3
%A A353000 _Bernard Schott_, Apr 14 2022
%E A353000 More terms from _Amiram Eldar_, Apr 14 2022