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A344908 Sum of the distinct odd-indexed prime divisors, p_{2k-1}, of n. 2
0, 2, 0, 2, 5, 2, 0, 2, 0, 7, 11, 2, 0, 2, 5, 2, 17, 2, 0, 7, 0, 13, 23, 2, 5, 2, 0, 2, 0, 7, 31, 2, 11, 19, 5, 2, 0, 2, 0, 7, 41, 2, 0, 13, 5, 25, 47, 2, 0, 7, 17, 2, 0, 2, 16, 2, 0, 2, 59, 7, 0, 33, 0, 2, 5, 13, 67, 19, 23, 7, 0, 2, 73, 2, 5, 2, 11, 2, 0, 7, 0, 43, 83, 2, 22 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(m) = 0 for m in A066207. - Michel Marcus, Jun 12 2021

LINKS

Martin Ehrenstein, Table of n, a(n) for n = 1..20000

FORMULA

a(n) = Sum_{p|n} p * (pi(p) mod 2).

EXAMPLE

a(6) = Sum_{p|6} p * (pi(p) mod 2) = 2*(pi(2) mod 2) + 3*(pi(3) mod 2) = 2*1 + 3*0 = 2.

MATHEMATICA

Table[Sum[k*Mod[PrimePi[k], 2] (PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 100}]

PROG

(PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, if (primepi(f[k, 1]) % 2, f[k, 1])); \\ Michel Marcus, Jun 12 2021

CROSSREFS

Cf. A000720 (pi), A008472 (sopf), A005074, A066207, A324966.

Cf. A344931 (sum of distinct even-indexed prime divisors).

Sequence in context: A324045 A209701 A158855 * A005074 A161564 A078182

Adjacent sequences:  A344905 A344906 A344907 * A344909 A344910 A344911

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Jun 02 2021

STATUS

approved

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Last modified September 17 01:53 EDT 2021. Contains 347478 sequences. (Running on oeis4.)