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

%I A035321 #12 Jul 08 2025 21:33:01
%S A035321 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,
%T A035321 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,
%U A035321 55,98,57,58,0,153,0,62,84,0,65,127,0,102,69,129,0,168,0,74,90,114,77
%N A035321 Sum of composite divisors of n that are not primes nor prime powers.
%H A035321 Antti Karttunen, <a href="/A035321/b035321.txt">Table of n, a(n) for n = 1..65537</a>
%F A035321 a(n) = A178637(n) - 1. - _Antti Karttunen_, Aug 06 2018
%p A035321 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;
%t A035321 Array[ Plus @@ (Select[ Divisors[ # ], (Length[ FactorInteger[ # ] ]>1)& ])&, 80 ]
%o A035321 (PARI) A035321(n) = sumdiv(n,d,(omega(d)>1)*(d)); \\ _Antti Karttunen_, Aug 06 2018
%Y A035321 Cf. A000203, A035322, A023891, A060278.
%Y A035321 One less than A178637.
%K A035321 nonn
%O A035321 1,6
%A A035321 _N. J. A. Sloane_
%E A035321 Description corrected by _Jack Brennen_, Mar 28 2001