A326697 - OEIS

%I #16 Sep 08 2022 08:46:24

%S 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 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 3,1,1,1,1,1,12,1,1,1,1,1,3,1,1,1,1,1,28

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

%C a(A097603(n)) > 1.

%C See A173441 and A326698 for number and product such divisors.

%C From _Bernard Schott_, Aug 13 2019: (Start)

%C a(n) = 1 if n is in A000961,

%C a(n) = 1 if n is in A006881 \ {6},

%C a(n) = 1 if n is in A001749 \ {12, 28}. (End)

%H Antti Karttunen, <a href="/A326697/b326697.txt">Table of n, a(n) for n = 1..20000</a>

%e For n = 12, divisors d of 12: 1, 2, 3, 4, 6, 12;

%e corresponding sigma(d): 1, 3, 4, 7, 12, 28;

%e sigma(d) divides n for 4 divisors d: 1, 2, 3, 6;

%e a(12) = 1 + 2 + 3 + 6 = 12.

%t a[n_] := DivisorSum[n, # &, Divisible[n, DivisorSigma[1, #]] &]; Array[a, 100] (* _Amiram Eldar_, Jul 21 2019 *)

%o (Magma) [&+[d: d in Divisors(n) | IsIntegral(n / SumOfDivisors(d))]: n in [1..100]]

%o (PARI) a(n) = sumdiv(n, d, d*(!(n % sigma(d)))); \\ _Michel Marcus_, Jul 19 2019

%Y Cf. A000203, A000961, A173441, A326698.

%K nonn

%O 1,6

%A _Jaroslav Krizek_, Jul 19 2019