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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)); 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.)