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

Author

Amiram Eldar, Sep 14 2023

Keywords

• nonn
• easy
• mult

Links

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

Crossrefs

Cf. A072873, A365637.

Programs

Mathematica

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

PARI

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

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... .

Extensions

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