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

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, 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, 3, 1, 1, 1, 1, 1, 12, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 28

Offset

1,6

Comments

a(A097603(n)) > 1.

See A173441 and A326698 for number and product such divisors.

From Bernard Schott, Aug 13 2019: (Start)

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

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

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Example

For n = 12, divisors d of 12: 1, 2, 3, 4, 6, 12;
corresponding sigma(d): 1, 3, 4, 7, 12, 28;
sigma(d) divides n for 4 divisors d: 1, 2, 3, 6;
a(12) = 1 + 2 + 3 + 6 = 12.

Mathematica

a[n_] := DivisorSum[n, # &, Divisible[n, DivisorSigma[1, #]] &]; Array[a, 100] (* Amiram Eldar, Jul 21 2019 *)

Prog

(Magma) [&+[d: d in Divisors(n) | IsIntegral(n / SumOfDivisors(d))]: n in [1..100]]
(PARI) a(n) = sumdiv(n, d, d*(!(n % sigma(d)))); \\ Michel Marcus, Jul 19 2019

Crossrefs

Cf. A000203, A000961, A173441, A326698.

Sequence in context: A135939 A061653 A069226 * A366168 A016565 A051714

Adjacent sequences: A326694 A326695 A326696 * A326698 A326699 A326700

Keyword

nonn

Author

Jaroslav Krizek, Jul 19 2019

Status

approved