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 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. 1
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,32 LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 Index entries for sequences computed from exponents in factorization of n FORMULA a(n) = A001055(n) - A033273(n). MATHEMATICA 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 *) PROG (PARI) 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}; A001055(n) = fcnt(n, n); \\ This function from Michael B. Porter, Oct 29 2009 A167688(n) = A001055(n) - (numdiv(n) - omega(n)); \\ Antti Karttunen, Jul 12 2017 CROSSREFS Cf. A001055, A033273. Sequence in context: A227344 A130207 A325433 * A083914 A083891 A363860 Adjacent sequences: A167685 A167686 A167687 * A167689 A167690 A167691 KEYWORD nonn AUTHOR Juri-Stepan Gerasimov, Nov 09 2009 EXTENSIONS a(64) and a(80) corrected by R. J. Mathar, May 30 2010 STATUS approved

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Last modified June 13 17:32 EDT 2024. Contains 373391 sequences. (Running on oeis4.)