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A189120 Sum of squares of nonprime divisors of n.

%I A189120 #18 Sep 04 2022 12:23:14
%S A189120 1,1,1,17,1,37,1,81,82,101,1,197,1,197,226,337,1,442,1,517,442,485,1,
%T A189120 837,626,677,811,997,1,1262,1,1361,1090,1157,1226,1898,1,1445,1522,
%U A189120 2181,1,2438,1,2437,2332,2117,1,3397,2402,3226,2602,3397,1,4087,3026,4197,3250,3365
%N A189120 Sum of squares of nonprime divisors of n.
%C A189120 a(p) = 1 for p prime.
%H A189120 Robert Israel, <a href="/A189120/b189120.txt">Table of n, a(n) for n = 1..10000</a>
%F A189120 a(n) = Sum_{k|n, k not prime} k^2.
%F A189120 G.f.: Sum_{k>=1} k^2*x^(k+1)/(1 - x^k) - prime(k)^2*x^(prime(k)+1)/(1 - x^prime(k)). - _Ilya Gutkovskiy_, Jan 01 2017
%F A189120 a(n) = A001157(n) - A005063(n). - _Wesley Ivan Hurt_, Sep 04 2022
%e A189120 a(12) = 197 because the divisors of 12 are {1, 2, 3, 4, 6, 12}, the subset of nonprime divisors are {1, 4, 6, 12}, and 1^2 + 4^2 + 6^2 + 12^2 = 197.
%p A189120 A189120 := proc(n) local a,d; a := 0 ; for d in numtheory[divisors](n) do if not isprime(d) then a := a+d^2 ; end if; end do: a ; end proc: # _R. J. Mathar_, Apr 17 2011
%t A189120 Table[Total[Select[Divisors[n], ! PrimeQ[#] &]^2], {n, 50}]
%Y A189120 Cf. A023890 (sum of the nonprime divisors of n).
%Y A189120 Cf. A001157, A005063.
%K A189120 nonn,easy
%O A189120 1,4
%A A189120 _Jonathan Vos Post_, Apr 17 2011