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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
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
Sequence in context: A253367 A253360 A252363 * A038857 A137632 A259740
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 February 25 19:44 EST 2024. Contains 370332 sequences. (Running on oeis4.)