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 A356193 a(n) is the smallest cubefull number (A036966) that is a multiple of n. 9
 1, 8, 27, 8, 125, 216, 343, 8, 27, 1000, 1331, 216, 2197, 2744, 3375, 16, 4913, 216, 6859, 1000, 9261, 10648, 12167, 216, 125, 17576, 27, 2744, 24389, 27000, 29791, 32, 35937, 39304, 42875, 216, 50653, 54872, 59319, 1000, 68921, 74088, 79507, 10648, 3375, 97336 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS First differs from A053149 and A356192 at n=16. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 FORMULA Multiplicative with a(p^e) = p^max(e,3). a(n) = n iff n is in A036966. Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + (3*p-2)/(p^3*(p-1))) = 1.76434793373691907811... . - Amiram Eldar, Jul 29 2022 Sum_{k=1..n} a(k) ~ c * n^4, where c = (zeta(3)/4) * Product_{p prime} (1 - 1/p^2 - 1/p^3 + 2/p^5 - 1/p^6 - 1/p^8 + 2/p^9 - 1/p^10) = 0.1559111567... . - Amiram Eldar, Nov 13 2022 a(n) = n * A360541(n). - Amiram Eldar, Sep 01 2023 MATHEMATICA f[p_, e_] := p^Max[e, 3]; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 50] PROG (PARI) a(n) = {my(f=factor(n)); prod(i=1, #f~, f[i, 1]^max(f[i, 2], 3))}; CROSSREFS Cf. A002117, A036966, A360541. Similar sequences: A053143, A053149, A053167, A066638, A087320, A087321, A197863, A356191, A356192, A356194. Sequence in context: A088378 A005064 A056551 * A356192 A367934 A053149 Adjacent sequences: A356190 A356191 A356192 * A356194 A356195 A356196 KEYWORD nonn,easy,mult AUTHOR Amiram Eldar, Jul 29 2022 STATUS approved

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Last modified May 19 19:45 EDT 2024. Contains 372703 sequences. (Running on oeis4.)