A167688 - OEIS

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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.

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

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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 * A376679 A083914 A083891

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