OFFSET
1,2
COMMENTS
Partial sums of A045778.
LINKS
Eric Weisstein's World of Mathematics, Unordered Factorization
FORMULA
a(p^k) = a(p^k-1) + A000009(k), where p is a prime.
EXAMPLE
a(6) = 7 because we have [1], [2], [3], [4], [5], [2*3] and [6] (the factorization [2*2] is not permitted because the factor 2 is present twice).
MATHEMATICA
Accumulate[gd[m_, 1] := 1; gd[1, n_] := 0; gd[1, 1] := 1; gd[0, n_] := 0; gd[m_, n_] := gd[m, n] = Total[gd[# - 1, n/#] & /@ Select[Divisors[n], # <= m &]]; Array[ gd[#, #] &, 75]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 26 2017
STATUS
approved