A365637 a(n) is the smallest number k such that k*n is a term of A072873.

1, 2, 9, 1, 625, 18, 117649, 2, 3, 1250, 25937424601, 9, 23298085122481, 235298, 5625, 1, 48661191875666868481, 6, 104127350297911241532841, 625, 1058841, 51874849202, 907846434775996175406740561329, 18, 125, 46596170244962, 1, 117649, 88540901833145211536614766025207452637361

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) - e).

a(n) = A365636(n)/n.

a(n) >= 1 with equality if and only if n is in A072873.

Mathematica

f[p_, e_] := p^(Ceiling[e/p]*p - e); 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]) - f[i, 2])); }

Crossrefs

Cf. A072873, A365636.

Sequence in context: A289632 A269919 A178418 * A249270 A153739 A298589

Adjacent sequences: A365634 A365635 A365636 * A365638 A365639 A365640

Keyword

nonn,easy,mult

Author

Amiram Eldar, Sep 14 2023

Extensions

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

Status

approved