cp's OEIS Frontend

A167688 Number of ways of factoring n with all factors greater than 1 (a(1)=1 by convention) minus number of nonprime divisors of n.

%I A167688 #10 Jul 13 2017 21:13:53
%S A167688 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,2,0,0,
%T A167688 0,2,0,0,0,1,0,0,0,0,0,0,0,4,0,0,0,0,0,1,0,1,0,0,0,2,0,0,0,5,0,0,0,0,
%U A167688 0,0,0,6,0,0,0,0,0,0,0,4,1,0,0,2,0,0,0,1,0,2,0,0,0,0,0,9,0,0,0,2,0,0,0,1,0
%N A167688 Number of ways of factoring n with all factors greater than 1 (a(1)=1 by convention) minus number of nonprime divisors of n.
%H A167688 Antti Karttunen, <a href="/A167688/b167688.txt">Table of n, a(n) for n = 1..10000</a>
%H A167688 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F A167688 a(n) = A001055(n) - A033273(n).
%t A167688 c[1, r_] := c[1, r] = 1; c[n_, r_] := c[n, r] = Module[{d, i}, d = Select[Divisors@ n, 1 < # <= r &]; Sum[c[n/d[[i]], d[[i]]], {i, 1, Length@ d}]]; Array[c[#, #] - DivisorSum[#, 1 &, ! PrimeQ@ # &] &, 105] (* _Michael De Vlieger_, Jul 12 2017, after _Dean Hickerson_ at A001055 *)
%o A167688 (PARI)
%o A167688 fcnt(n, m) = {local(s); s=0; if(n == 1, s=1, fordiv(n, d, if((d > 1) && (d <= m), s=s+fcnt(n/d, d)))); s};
%o A167688 A001055(n) = fcnt(n, n); \\ This function from _Michael B. Porter_, Oct 29 2009
%o A167688 A167688(n) = A001055(n) - (numdiv(n) - omega(n)); \\ _Antti Karttunen_, Jul 12 2017
%Y A167688 Cf. A001055, A033273.
%K A167688 nonn
%O A167688 1,32
%A A167688 _Juri-Stepan Gerasimov_, Nov 09 2009
%E A167688 a(64) and a(80) corrected by _R. J. Mathar_, May 30 2010