A388006 Numbers k = p_i^e_i *...* p_r^e_r such that i/e_i +...+ r/e_r = 1 for e_i,..., e_r >= 1; p_i,..., p_r distinct prime numbers (A000040).

2, 9, 125, 216, 324, 2401, 10000, 62500, 161051, 537824, 759375, 941192, 1265625, 4100625, 4826809, 23059204, 52734375, 85766121, 113379904, 410338673, 466948881, 729000000, 992436543, 1640250000, 3888000000, 5904900000, 8031810176, 8100000000, 10125000000

Offset

1,1

Comments

For k = p_i^i we have i/i = 1, thus A062457 is a subsequence of this sequence.

Links

Sean A. Irvine, Table of n, a(n) for n = 1..1000

Example

For k = 125 = 5^3 we have 3/3 = 1 thus k = 125 is a term.
For k = 216 = 2^3 * 3^3 we have 1/3 + 2/3 = 1 thus k = 216 is a term.

Prog

(PARI) isok(k) = my(f=factor(k)); sum(i=1, #f~, primepi(f[i, 1])/f[i, 2]) == 1; \\ Michel Marcus, Oct 14 2025

Crossrefs

Cf. A000040, A062457, A387978.

Sequence in context: A135543 A372745 A316855 * A088862 A062457 A307539

Adjacent sequences: A388003 A388004 A388005 * A388007 A388008 A388009

Keyword

nonn

Author

Ctibor O. Zizka, Oct 14 2025

Status

approved