cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A248816 Numbers that are equal to the arithmetic derivative of the sum of their aliquot parts.

This page as a plain text file.
%I A248816 #23 May 29 2024 03:17:47
%S A248816 152,284,4316,18632,25484,2657259,8394752,12186976,17702756,
%T A248816 1172473731,2147581952,13716855652,63831498112
%N A248816 Numbers that are equal to the arithmetic derivative of the sum of their aliquot parts.
%C A248816 Solutions of the equations n = (sigma(n)-n)'.
%C A248816 a(12) > 5*10^9. - _Michel Marcus_, Nov 01 2014
%C A248816 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 A248816 a(14) > 10^11. - _Giovanni Resta_, May 29 2016
%e A248816 Sum of the aliquot parts of 284 is sigma(284) - 284 = 220 and the arithmetic derivative of 220 is 284.~
%p A248816 with(numtheory): P:= proc(q) local a,n,p; for n from 1 to q do
%p A248816 a:=(sigma(n)-n)*add(op(2,p)/op(1,p),p=ifactors(sigma(n)-n)[2]);
%p A248816 if n=a then print(n); fi; od; end: P(10^9);
%o A248816 (PARI) ad(n) = sum(i=1, #f=factor(n)~, n/f[1, i]*f[2, i]);
%o A248816 isok(n) = ad(sigma(n) - n) == n; \\ _Michel Marcus_, Oct 28 2014
%Y A248816 Cf. A000203, A003415, A230164.
%K A248816 nonn,more
%O A248816 1,1
%A A248816 _Paolo P. Lava_, Oct 15 2014
%E A248816 a(6)-a(11) from _Michel Marcus_, Oct 28 2014
%E A248816 a(12)-a(13) from _Giovanni Resta_, May 29 2016