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 A366145 The number of divisors of the largest divisor of n that is a cubefull number (A036966). 5
 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 4, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 4, 1, 4, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 5, 5, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 FORMULA a(n) = A000005(A360540(n)). a(n) = A000005(n)/A366147(n). a(n) >= 1, with equality if and only if n is cubefree (A004709). a(n) <= A000005(n), with equality if and only if n is cubefull (A036966). Multiplicative with a(p^e) = 1 if e <= 2 and e+1 otherwise. Dirichlet g.f.: zeta(s)^2 * Product_{p prime} (1 - 1/p^s + 3/p^(3*s) - 2/p^(4*s)). Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = zeta(2) * Product_{p prime} (1 - 1/p^2 + 3/p^3 + 1/p^4 - 2/p^5) = 1.76434793373691907811... . MATHEMATICA f[p_, e_] := If[e < 3, 1, e+1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] PROG (PARI) a(n) = vecprod(apply(x -> if(x < 3, 1, x+1), factor(n)[, 2])); CROSSREFS Cf. A000005, A036966, A357669, A360540, A366076, A366146, A366147. Sequence in context: A368172 A359594 A368331 * A204160 A360165 A336870 Adjacent sequences: A366142 A366143 A366144 * A366146 A366147 A366148 KEYWORD nonn,easy,mult AUTHOR Amiram Eldar, Oct 01 2023 STATUS approved

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Last modified August 2 19:53 EDT 2024. Contains 374875 sequences. (Running on oeis4.)