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A326697 a(n) is the sum of divisors d of n such that sigma(d) divides n.

%I A326697 #23 Mar 17 2025 15:56:47
%S A326697 1,1,1,1,1,3,1,1,1,1,1,12,1,1,1,1,1,3,1,1,1,1,1,12,1,1,1,5,1,8,1,1,1,
%T A326697 1,1,12,1,1,1,1,1,3,1,1,1,1,1,12,1,1,1,1,1,3,1,40,1,1,1,17,1,1,1,1,1,
%U A326697 3,1,1,1,1,1,12,1,1,1,1,1,3,1,1,1,1,1,28
%N A326697 a(n) is the sum of divisors d of n such that sigma(d) divides n.
%C A326697 a(A097603(n)) > 1.
%C A326697 See A173441 and A326698 for number and product of such divisors.
%C A326697 From _Bernard Schott_, Aug 13 2019: (Start)
%C A326697 a(n) = 1 if n is in A000961,
%C A326697 a(n) = 1 if n is in A006881 \ {6},
%C A326697 a(n) = 1 if n is in A001749 \ {12, 28}. (End)
%H A326697 Antti Karttunen, <a href="/A326697/b326697.txt">Table of n, a(n) for n = 1..20000</a>
%e A326697 For n = 12, divisors d of 12: 1, 2, 3, 4, 6, 12;
%e A326697 corresponding sigma(d): 1, 3, 4, 7, 12, 28;
%e A326697 sigma(d) divides n for 4 divisors d: 1, 2, 3, 6;
%e A326697 a(12) = 1 + 2 + 3 + 6 = 12.
%t A326697 a[n_] := DivisorSum[n, # &, Divisible[n, DivisorSigma[1, #]] &]; Array[a, 100] (* _Amiram Eldar_, Jul 21 2019 *)
%o A326697 (Magma) [&+[d: d in Divisors(n) | IsIntegral(n / SumOfDivisors(d))]: n in [1..100]];
%o A326697 (PARI) a(n) = sumdiv(n, d, d*(!(n % sigma(d)))); \\ _Michel Marcus_, Jul 19 2019
%Y A326697 Cf. A000203, A000961, A173441, A326698.
%K A326697 nonn
%O A326697 1,6
%A A326697 _Jaroslav Krizek_, Jul 19 2019