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Convolution of natural numbers with composite numbers.
2

%I #11 Jul 18 2021 03:15:37

%S 4,14,32,59,96,145,208,286,380,492,624,777,952,1151,1375,1625,1902,

%T 2207,2542,2909,3309,3743,4212,4717,5260,5842,6464,7128,7836,8589,

%U 9388,10235,11131,12077,13074,14123,15226,16384,17598,18869,20198

%N Convolution of natural numbers with composite numbers.

%H Seiichi Manyama, <a href="/A023539/b023539.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1) = 1*4 = 4;

%e a(2) = 1*6 + 2*4 = 14;

%e a(3) = 1*8 + 2*6 + 3*4 = 32;

%o (PARI) lista(nn) = {my(vc = []); forcomposite(n=2, nn, vc = concat(vc, n); print1(sum(k=1, #vc, (#vc-k+1)*vc[k]), ", "););} \\ _Michel Marcus_, Feb 11 2018

%Y Cf. A002808.

%Y First differences are in A053767.

%K nonn

%O 1,1

%A _Clark Kimberling_