A326990 Sum of odd divisors of n that are greater than 1.

0, 0, 3, 0, 5, 3, 7, 0, 12, 5, 11, 3, 13, 7, 23, 0, 17, 12, 19, 5, 31, 11, 23, 3, 30, 13, 39, 7, 29, 23, 31, 0, 47, 17, 47, 12, 37, 19, 55, 5, 41, 31, 43, 11, 77, 23, 47, 3, 56, 30, 71, 13, 53, 39, 71, 7, 79, 29, 59, 23, 61, 31, 103, 0, 83, 47, 67, 17, 95, 47, 71, 12, 73, 37, 123, 19, 95, 55, 79, 5

Offset

1,3

Comments

Also sum of nonpowers of 2 dividing n, divided the sum of powers of 2 dividing n.

a(n) = 0 iff n is a power of 2.

a(n) = n iff n is an odd prime.

First differs from A284233 at a(15).

Links

Table of n, a(n) for n=1..80.

Formula

a(n) = A000593(n) - 1.

a(n) = (A000203(n) - A038712(n))/A038712(n).

a(n) = A326988(n)/A038712(n).

Example

For n = 18 the divisors of 18 are [1, 2, 3, 6, 9, 18]. The sum of odd divisors of 18 that are greater than 1 is 3 + 9 = 12, so a(18) = 12. On the other hand, there are four divisors of 18 that are not powers of 2, they are [3, 6, 9, 18], and the sum of them is 3 + 6 + 9, 18 = 36. Also there are two divisors of 18 that are powers of 2, they are [1, 2], and the sum of them is 1 + 2 = 3. Then we have that 36/3 = 12, so a(18) = 12.

Prog

(Magma) sol:=[]; m:=1; for n in [1..80] do v:=[d:d in Divisors(n)|d gt 1 and IsOdd(d)]; if #v ne 0 then sol[m]:=&+v; m:=m+1; else sol[m]:=0; m:=m+1; end if; end for; sol; // Marius A. Burtea, Aug 24 2019

Crossrefs

Cf. A000079, A000203, A000593, A038712, A057716, A065091, A069283 (Number), A284233, A326988, A326989.

Sequence in context: A005069 A366840 A284233 * A037284 A225058 A002123

Adjacent sequences: A326987 A326988 A326989 * A326991 A326992 A326993

Keyword

nonn

Author

Omar E. Pol, Aug 24 2019

Status

approved