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%I #21 May 29 2016 07:05:25
%S 152,284,4316,18632,25484,2657259,8394752,12186976,17702756,
%T 1172473731,2147581952,13716855652,63831498112
%N Numbers that are equal to the arithmetic derivative of the sum of their aliquot parts.
%C Solutions of the equations n = (sigma(n)-n)'.
%C a(12) > 5*10^9. - _Michel Marcus_, Nov 01 2014
%C There could be a relation with terms in A125246 and A228450, since some terms of these sequences are here also. - _Michel Marcus_, Oct 30 2014
%C a(14) > 10^11. - _Giovanni Resta_, May 29 2016
%F Sum of the aliquot parts of 284 is sigma(284) - 284 = 220 and the arithmetic derivative of 220 is 284.
%p with(numtheory): P:= proc(q) local a,n,p; for n from 1 to q do
%p a:=(sigma(n)-n)*add(op(2,p)/op(1,p),p=ifactors(sigma(n)-n)[2]);
%p if n=a then print(n); fi; od; end: P(10^9);
%o (PARI) ad(n) = sum(i=1, #f=factor(n)~, n/f[1, i]*f[2, i]);
%o isok(n) = ad(sigma(n) - n) == n; \\ _Michel Marcus_, Oct 28 2014
%Y Cf. A000203, A003415, A230164.
%K nonn,more
%O 1,1
%A _Paolo P. Lava_, Oct 15 2014
%E a(6)-a(11) from _Michel Marcus_, Oct 28 2014
%E a(12)-a(13) from _Giovanni Resta_, May 29 2016
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