A035321 Sum of composite divisors of n that are not primes nor prime powers.

0, 0, 0, 0, 0, 6, 0, 0, 0, 10, 0, 18, 0, 14, 15, 0, 0, 24, 0, 30, 21, 22, 0, 42, 0, 26, 0, 42, 0, 61, 0, 0, 33, 34, 35, 72, 0, 38, 39, 70, 0, 83, 0, 66, 60, 46, 0, 90, 0, 60, 51, 78, 0, 78, 55, 98, 57, 58, 0, 153, 0, 62, 84, 0, 65, 127, 0, 102, 69, 129, 0, 168, 0, 74, 90, 114, 77

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A000203, A035322, A023891, A060278.

One less than A178637.

Programs

Maple

pp := array(1..100); for i from 1 to 100 do pp[i] := 0; od: for i from 1 to 25 do for j from 1 to 6 do t1 := ithprime(i)^j; if t1<100 then pp[t1] := 1; fi; od: od: pp[1] := 1; A035321 := proc(n) local i,d,t1,t2; t1 := 0; for d from 1 to n do if n mod d = 0 and pp[d] = 0 then t1 := t1+d; fi; od; t1; end;

Mathematica

Array[ Plus @@ (Select[ Divisors[ # ], (Length[ FactorInteger[ # ] ]>1)& ])&, 80 ]

PARI

A035321(n) = sumdiv(n,d,(omega(d)>1)*(d)); \\ Antti Karttunen, Aug 06 2018

Formula

a(n) = A178637(n) - 1. - Antti Karttunen, Aug 06 2018

Extensions

Description corrected by Jack Brennen, Mar 28 2001