

A248816


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


0



152, 284, 4316, 18632, 25484, 2657259, 8394752, 12186976, 17702756, 1172473731, 2147581952, 13716855652, 63831498112
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OFFSET

1,1


COMMENTS

Solutions of the equations n = (sigma(n)n)'.
a(12) > 5*10^9.  Michel Marcus, Nov 01 2014
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
a(14) > 10^11.  Giovanni Resta, May 29 2016


LINKS

Table of n, a(n) for n=1..13.


FORMULA

Sum of the aliquot parts of 284 is sigma(284)  284 = 220 and the arithmetic derivative of 220 is 284.


MAPLE

with(numtheory): P:= proc(q) local a, n, p; for n from 1 to q do
a:=(sigma(n)n)*add(op(2, p)/op(1, p), p=ifactors(sigma(n)n)[2]);
if n=a then print(n); fi; od; end: P(10^9);


PROG

(PARI) ad(n) = sum(i=1, #f=factor(n)~, n/f[1, i]*f[2, i]);
isok(n) = ad(sigma(n)  n) == n; \\ Michel Marcus, Oct 28 2014


CROSSREFS

Cf. A000203, A003415, A230164.
Sequence in context: A253367 A253360 A252363 * A038857 A137632 A259740
Adjacent sequences: A248813 A248814 A248815 * A248817 A248818 A248819


KEYWORD

nonn,more


AUTHOR

Paolo P. Lava, Oct 15 2014


EXTENSIONS

a(6)a(11) from Michel Marcus, Oct 28 2014
a(12)a(13) from Giovanni Resta, May 29 2016


STATUS

approved



