OFFSET
1,9
COMMENTS
Number of parts larger than 1 in the partition with Heinz number n. The Heinz number of an integer partition p = [p_1, p_2, ..., p_r] is defined as Product(p_j-th prime, j=1...r) (concept used by Alois P. Heinz in A215366 as an "encoding" of a partition). Example: a(9) = 2 because the partition with Heinz number 9 (=3*3) is [2,2]. - Emeric Deutsch, Oct 02 2015
Totally additive because both A001222 and A007814 are. a(2) = 0, and a(p) = 1 for odd primes p, a(m*n) = a(m)+a(n) for m, n > 1. - Antti Karttunen, Jul 10 2020
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..65537 (first 1000 terms from G. C. Greubel)
FORMULA
EXAMPLE
a(9) = 2 because 9 = 3*3 has 2 odd prime factors. - Emeric Deutsch, Oct 02 2015
MAPLE
seq(bigomega(n) - padic[ordp](n, 2), n=1..102); # Peter Luschny, Dec 06 2017
MATHEMATICA
Join[{0}, Table[Length[Select[Flatten[Table[#[[1]], {#[[2]]}]&/@ FactorInteger[ n]], OddQ]], {n, 2, 110}]] (* Harvey P. Dale, Feb 01 2013 *)
PROG
(PARI) a(n) = bigomega(n) - valuation(n, 2); \\ Michel Marcus, Sep 10 2019
(PARI) A087436(n) = (bigomega(n>>valuation(n, 2))); \\ Antti Karttunen, Jul 10 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Sep 03 2003
STATUS
approved