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A193523 Number of odd divisors of Sopf(n). 2
0, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 3, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 3, 2, 2, 2, 1, 2, 2, 2, 2, 2, 4, 1, 2, 2, 2, 2, 2, 1, 3, 2, 2, 2, 2, 2, 4, 2, 2, 1, 3, 2, 2, 2, 2, 2, 4, 2, 1, 3, 1, 2, 2, 2, 2, 2, 2, 2, 4, 1, 4, 3, 3, 2, 2, 2, 2, 2, 2, 2, 6, 1, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 4, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Sopf(n) is the sum of the distinct primes dividing n (A008472).

LINKS

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

FORMULA

a(1) = 0; for n > 1, a(n) = A001227(A008472(n)). - Antti Karttunen, Dec 23 2018

EXAMPLE

a(26) = 4 because Sopf(26) = 15 and the 4 odd divisors are {1, 3, 5, 15}.

MATHEMATICA

f[n_] := Block[{d=Divisors[Plus@@First[Transpose[FactorInteger[n]]]]}, Count[OddQ[d], True]]; Table[f[n], {n, 100}]

PROG

(PARI)

A001227(n) = numdiv(n>>valuation(n, 2));

A008472(n) = vecsum(factor(n)[, 1]); \\ From A008472

A193523(n) = if(1==n, 0, A001227(A008472(n))); \\ Antti Karttunen, Dec 23 2018

CROSSREFS

Cf. A001227, A008472.

Sequence in context: A099812 A246600 A068068 * A092505 A066086 A323406

Adjacent sequences:  A193520 A193521 A193522 * A193524 A193525 A193526

KEYWORD

nonn

AUTHOR

Michel Lagneau, Jul 29 2011

EXTENSIONS

More terms from Antti Karttunen, Dec 23 2018

STATUS

approved

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Last modified March 8 13:59 EST 2021. Contains 341949 sequences. (Running on oeis4.)