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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 24 04:19 EDT 2020. Contains 337317 sequences. (Running on oeis4.)