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 A269459 Numbers that are equal to the sum of the number of divisors of their first k arithmetic derivatives, for some k. 0
 15, 16, 45, 60, 69, 75, 112, 116, 236, 296, 319, 452, 576, 586, 843, 1047, 1184, 1704, 1902, 2852, 2966, 3068, 3122, 4708, 4805, 5684, 6150, 6712, 7126, 10920, 10950, 13107, 16700, 18698 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS EXAMPLE The first eight arithmetic derivatives of 75 are 55, 16, 32, 80, 176, 368, 752, 1520 and d(55) + d(16) + d(32) + d(80) + d(176) + d(368) + d(752) + d(1520) = 4 + 5 + 6 + 10 + 10 + 10 + 10 + 20 = 75. MAPLE with(numtheory): P:=proc(q) local a, b, k, n, p; for n from 1 to q do a:=0; k:=1; b:=n; while a0 then a:=a+tau(b); else break; fi; od; if n=a then print(n); fi; od; end: P(10^6); PROG (PARI) ad(n) = if (n<1, 0, my(f = factor(n)); n*sum(k=1, #f~, f[k, 2]/f[k, 1])); isok(n) = {ss = 0; kn = n; while (ss < n, der = ad(kn); if (der == 0, break); ss += numdiv(der); kn = der); ss == n; } \\ Michel Marcus, Apr 08 2016 CROSSREFS Cf. A000005, A003415, A270389, A270713. Sequence in context: A041450 A042867 A296863 * A041462 A041464 A041460 Adjacent sequences:  A269456 A269457 A269458 * A269460 A269461 A269462 KEYWORD nonn,more AUTHOR Paolo P. Lava, Apr 06 2016 STATUS approved

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Last modified January 16 15:31 EST 2019. Contains 319195 sequences. (Running on oeis4.)