A193523 Number of odd divisors of Sopf(n).

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

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