A356193 a(n) is the smallest cubefull number (A036966) that is a multiple of n.

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

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