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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. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,6
LINKS
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
Sequence in context: A222328 A222402 A222522 * A037285 A337981 A341761
KEYWORD
easy,nonn,look
AUTHOR
Mohammad K. Azarian, Mar 16 2004
STATUS
approved

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Last modified June 14 15:00 EDT 2024. Contains 373400 sequences. (Running on oeis4.)