A365636 a(n) is the smallest multiple of n that is a term of A072873.

1, 4, 27, 4, 3125, 108, 823543, 16, 27, 12500, 285311670611, 108, 302875106592253, 3294172, 84375, 16, 827240261886336764177, 108, 1978419655660313589123979, 12500, 22235661, 1141246682444, 20880467999847912034355032910567, 432, 3125, 1211500426369012, 27, 3294172

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..388

Formula

Multiplicative with a(p^e) = p^(p*ceiling(e/p)).

a(n) = n * A365637(n).

a(n) >= n with equality if and only if n is in A072873.

Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + p/(p^p-1)) = 1.86196549645040699446... .

Mathematica

f[p_, e_] := p^(Ceiling[e/p]*p); a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 30]

Prog

(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^(f[i, 1] * ceil(f[i, 2] / f[i, 1]))); }

Crossrefs

Cf. A072873, A365637.

Sequence in context: A144990 A102199 A351366 * A345311 A125723 A094543

Adjacent sequences: A365633 A365634 A365635 * A365637 A365638 A365639

Keyword

nonn,easy,mult

Author

Amiram Eldar, Sep 14 2023

Extensions

Data, formulas and codes corrected by Amiram Eldar, Feb 15 2024

Status

approved