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 A259495 Numbers k such that sigma(k) + phi(k) + d(k) = sigma(k+1) + phi(k+1) + d(k+1), where sigma(k) is the sum of the divisors of k, phi(k) the Euler totient function of k and d(k) the number of divisors of k. 2
 4, 285, 902, 2013, 8493, 37406, 61918, 90094, 120001, 184484, 250550, 303853, 352941, 360446, 375565, 501693, 724934, 889285, 940093, 995630, 1079662, 1473565, 1488957, 1517206, 1573045, 1581806, 1692302, 1864285, 2048973, 2693517, 3393934, 3509997, 4083526, 4194406 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Amiram Eldar, Table of n, a(n) for n = 1..100 EXAMPLE sigma(4) + phi(4) + d(4) = 7 + 2 + 3 = 12 and sigma(5) + phi(5) + d(5) = 6 + 4 + 2 = 12. sigma(285) + phi(285) + d(285) = 480 + 144 + 8 = 632 and sigma(286) + phi(286) + d(286) = 504 + 120 + 8 = 632. MAPLE with(numtheory): P:=proc(q) local n; for n from 1 to q do if sigma(n)+phi(n)+tau(n)=sigma(n+1)+phi(n+1)+tau(n+1) then print(n); fi; od; end: P(10^9); MATHEMATICA f[n_] := Module[{fct = FactorInteger[n]}, p = fct[[All, 1]]; e = fct[[All, 2]]; Times @@ (e + 1) + Times @@ ((p^(e + 1) - 1)/(p - 1)) + Times @@ ((p - 1)*p^(e - 1))]; f1 = 0; s = {}; Do[f2 = f[n]; If[f2 == f1, AppendTo[s, n - 1]]; f1 = f2, {n, 2, 10^5}]; s (* Amiram Eldar, Jul 12 2019 *) CROSSREFS Cf. A000005, A000010, A000203, A233541. Cf. A054004, A145749, A259496. Sequence in context: A202031 A074309 A113256 * A090088 A253233 A242997 Adjacent sequences: A259492 A259493 A259494 * A259496 A259497 A259498 KEYWORD nonn AUTHOR Paolo P. Lava, Jun 29 2015 STATUS approved

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Last modified September 16 19:27 EDT 2024. Contains 375977 sequences. (Running on oeis4.)