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%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_.
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