A091921 Sum of odd proper distinct prime divisors of n. That is, the sum of odd distinct prime divisors of n that are less than n.

0, 0, 0, 0, 0, 3, 0, 0, 3, 5, 0, 3, 0, 7, 8, 0, 0, 3, 0, 5, 10, 11, 0, 3, 5, 13, 3, 7, 0, 8, 0, 0, 14, 17, 12, 3, 0, 19, 16, 5, 0, 10, 0, 11, 8, 23, 0, 3, 7, 5, 20, 13, 0, 3, 16, 7, 22, 29, 0, 8, 0, 31, 10, 0, 18, 14, 0, 17, 26, 12, 0, 3, 0, 37, 8, 19, 18, 16, 0, 5, 3, 41, 0, 10, 22, 43, 32, 11, 0

Offset

1,6

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

From Robert Israel, Jan 28 2018: (Start)

If n is even, a(n) = A008472(n)-2.

If n is prime, a(n) = A008472(n)-n = 0.

Otherwise, a(n) = A008472(n). (End)

Example

The sum of odd proper distinct prime divisors of 15 is 8=3+5.

Maple

seq(convert(numtheory:-factorset(n) minus {2, n}, `+`), n=1..100); # Robert Israel, Jan 28 2018

Mathematica

Table[Total[Select[Most[Divisors[n]], OddQ[#]&&PrimeQ[#]&]], {n, 90}] (* Harvey P. Dale, Dec 31 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, if ((d%2) && isprime(d) && (d<n), d)); \\ Michel Marcus, Jan 28 2018

Crossrefs

Cf. A008472, A091979, A001227.

Sequence in context: A222328 A222402 A222522 * A037285 A337981 A341761

Adjacent sequences: A091918 A091919 A091920 * A091922 A091923 A091924

Keyword

easy,nonn,look

Author

Mohammad K. Azarian, Mar 16 2004

Status

approved