login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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: A280129 A227344 A130207 * A083914 A083891 A087623

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 14 09:49 EST 2018. Contains 317182 sequences. (Running on oeis4.)