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

1,6

Links

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

Formula

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

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 ]

Prog

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

Crossrefs

Cf. A000203, A035322, A023891, A060278.

One less than A178637.

Sequence in context: A282212 A074591 A318877 * A028720 A028663 A028716

Adjacent sequences: A035318 A035319 A035320 * A035322 A035323 A035324

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

Description corrected by Jack Brennen, Mar 28 2001

Status

approved