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 A369720 The sum of divisors of the smallest cubefull number that is a multiple of n. 5
 1, 15, 40, 15, 156, 600, 400, 15, 40, 2340, 1464, 600, 2380, 6000, 6240, 31, 5220, 600, 7240, 2340, 16000, 21960, 12720, 600, 156, 35700, 40, 6000, 25260, 93600, 30784, 63, 58560, 78300, 62400, 600, 52060, 108600, 95200, 2340, 70644, 240000, 81400, 21960, 6240 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 FORMULA a(n) = A000203(A356193(n)). Multiplicative with a(p) = p^3 + p^2 + p + 1 for e <= 2, and a(p^e) = (p^(e+1)-1)/(p-1) for e >= 3. a(n) >= A000203(n), with equality if and only if n is cubefull (A036966). Dirichlet g.f.: zeta(s-1) * zeta(s) * Product_{p prime} (1 + 1/p^(s-3) + 1/p^(s-2) - 1/p^(2*s-4) - 1/p^(2*s-3) - 1/p^(2*s-2) + 1/p^(4*s-4)). Sum_{k=1..n} a(k) ~ c * n^4 / 4, where c = zeta(3) * zeta(4) * Product_{p prime} (1 - 1/p^3 - 1/p^4 + 1/p^7 + 1/p^12 - 1/p^13) = 1.00015013207437782094... . MATHEMATICA f[p_, e_] := (p^If[e <= 2, 4, e + 1]-1)/(p-1); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 50] PROG (PARI) a(n) = {my(f = factor(n)); for(i = 1, #f~, if(f[i, 2] <= 2, f[i, 2] = 3)); sigma(f); } CROSSREFS Cf. A000203, A036966, A356193, A369717, A369719, A369721. Cf. A002117, A013662, A183700. Sequence in context: A126950 A091847 A062222 * A369758 A325659 A223432 Adjacent sequences: A369717 A369718 A369719 * A369721 A369722 A369723 KEYWORD nonn,easy,mult AUTHOR Amiram Eldar, Jan 30 2024 STATUS approved

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Last modified June 13 17:15 EDT 2024. Contains 373391 sequences. (Running on oeis4.)