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%I #27 Sep 08 2022 08:46:09
%S 1,3,6,12,28,84,120,234,270,496,672,1080,1488,1638,6048,6552,8128,
%T 24384,30240,32760,35640,199584,435708,523776,2142720,2178540,4713984,
%U 12999168,18506880,23569920,33550336,36197280,45532800
%N Numbers k that divide 3*sigma(k).
%C Numbers k that divide 3*A000203(k).
%C Supersequence of A007691 and A245775.
%C Union of A007691 and 3*A227303. - _Robert Israel_, Aug 26 2014
%e Number 12 is in the sequence because 12 divides 3*sigma(12) = 3*28.
%p select(n -> 3*numtheory:-sigma(n) mod n = 0, [$1..10^6]); # _Robert Israel_, Aug 26 2014
%t a245774[n_Integer] := Select[Range[n], Divisible[3*DivisorSigma[1, #], #] == True &]; a245774[10^7] (* _Michael De Vlieger_, Aug 27 2014 *)
%o (Magma) [n: n in [1..3000000] | Denominator(3*(SumOfDivisors(n))/n) eq 1]
%o (PARI)
%o for(n=1,10^9,if((3*sigma(n))%n==0,print1(n,", "))) \\ _Derek Orr_, Aug 26 2014
%Y Cf. A000203 (sum of divisors), A007691 (multiply-perfect numbers).
%Y Cf. A227303 (n divides sigma(3n)), A245775 (denominator(sigma(n)/n) = 3).
%Y Cf. A272027 (3*sigma(n)).
%K nonn
%O 1,2
%A _Jaroslav Krizek_, Aug 26 2014