Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #16 Jul 13 2021 06:25:02
%S 4,10,42,90,2448,4680,27144,117000,154498509,222970077,11049088050,
%T 63554826816
%N Numbers m such that k*m = Sum_{j|m, j < m} sigma(j), where k >= 1 is an integer.
%C a(13) > 10^11.
%e The divisors of 10 smaller than 10 are 1, 2 and 5. Since sigma(1) + sigma(2) + sigma(5) = 10, 10 is in the sequence.
%t Select[Range[2, 120000], Mod[Total@DivisorSigma[1, Most@Divisors@#], #] == 0 &]
%o (PARI) isok(m) = sumdiv(m, d, if (d!=m, sigma(d))) % m == 0; \\ _Michel Marcus_, Jul 13 2021
%Y Cf. A211779, A221219.
%K nonn,more
%O 1,1
%A _Giovanni Resta_, Apr 08 2013
%E a(9)-a(12) and bound on a(13) from _Donovan Johnson_.