A050334 Number of ordered factorizations of n into numbers with an odd number of prime divisors (prime factors counted with multiplicity).
1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 2, 3, 1, 4, 1, 4, 2, 2, 1, 8, 1, 2, 2, 4, 1, 7, 1, 5, 2, 2, 2, 10, 1, 2, 2, 8, 1, 7, 1, 4, 4, 2, 1, 15, 1, 4, 2, 4, 1, 8, 2, 8, 2, 2, 1, 18, 1, 2, 4, 8, 2, 7, 1, 4, 2, 7, 1, 23, 1, 2, 4, 4, 2, 7, 1, 15, 3, 2, 1, 18, 2, 2, 2, 8, 1, 18, 2, 4, 2, 2, 2, 28, 1, 4, 4
Offset: 1
Keywords
Examples
From _R. J. Mathar_, May 25 2017: (Start) a(p) = 1: factorizations p. a(p^2) = 1: factorizations p*p. a(p^3) = 2: factorizations p^3, p*p*p. a(p^4) = 3: factorizations p^3*p, p*p^3, p*p*p*p. a(p^5) = 5: factorizations p^5, p^3*p*p, p*p^3*p, p*p*p^3, p*p*p*p*p. a(p*q) = 2: factorizations p*q, q*p. (End)
Links
- R. J. Mathar, Table of n, a(n) for n = 1..10000
Programs
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Maple
read(transforms): A066829m := proc(n) if n = 1 or isA026424(n) then 1; else 0; end if; end proc: [1,seq(-A066829m(n),n=2..10000)] ; DIRICHLETi(%) ; # R. J. Mathar, May 25 2017
Comments