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 A365633 The sum of divisors of n that are terms of A072873. 2
 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 7, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 4, 3, 1, 1, 1, 7, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 7, 1, 1, 1, 3, 1, 4, 1, 3, 1, 1, 1, 3, 1, 1, 1, 15, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 7, 4, 1, 1, 3, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS The number of these divisors is A365632(n) and the largest of them is A327939(n). LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 FORMULA Multiplicative with a(p^e) = (p^(floor(e/p)+1) - 1)/(p - 1). Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Product_{p prime} (A332653(p)/(p^(p-1)-1) - 1/(p*(p-1))) = 2.253624924813... . MATHEMATICA f[p_, e_] := (p^(Floor[e/p] + 1) - 1)/(p - 1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] PROG (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, (f[i, 1]^(1+f[i, 2] \ f[i, 1])-1)/(f[i, 1] - 1)); } CROSSREFS Cf. A072873, A327939, A332653, A365632. Sequence in context: A093148 A069292 A368336 * A091842 A306346 A060901 Adjacent sequences: A365630 A365631 A365632 * A365634 A365635 A365636 KEYWORD nonn,easy,mult AUTHOR Amiram Eldar, Sep 14 2023 STATUS approved

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Last modified September 10 19:55 EDT 2024. Contains 375794 sequences. (Running on oeis4.)