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%I #12 Jan 27 2023 19:51:38
%S 1,15,20,34,42,44,50,101,107,558,584,750,1491,2793,2889,15811,27285,
%T 60030,67258,87066
%N Numbers k such that the sum of the digits of sigma(k)^k is divisible by k.
%C Next term after 2889, if it exists, is greater than 10000.
%C Next term, if it exists, is greater than 30000. - _Sean A. Irvine_, Feb 24 2010
%C Next term, if it exists, is greater than 100000. - _Michael S. Branicky_, Jan 27 2023
%e The digits of sigma(1491)^1491 sum to 22365 and 22365 is divisible by 1491, so 1491 is in the sequence.
%t Do[s = DivisorSigma[1, n]^n; k = Plus @@ IntegerDigits[s]; If[Mod[k, n] == 0, Print[n]], {n, 1, 10000}]
%o (Python)
%o from sympy import divisor_sigma
%o def ok(n): return n and (sum(map(int, str(divisor_sigma(n, 1)**n)))%n == 0)
%o print([k for k in range(3000) if ok(k)]) # _Michael S. Branicky_, Jan 27 2023
%K base,more,nonn
%O 1,2
%A _Ryan Propper_, Aug 06 2005
%E a(16)-a(17) from _Sean A. Irvine_, Feb 24 2010
%E a(18)-a(20) from _Michael S. Branicky_, Jan 27 2023
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