A387978 Numbers k = p_i^e_i * p_j^e_j such that i/e_i + j/e_j = 1 for e_i, e_j >= 1, p_i, p_j distinct prime numbers.

216, 324, 10000, 62500, 537824, 759375, 941192, 1265625, 4100625, 23059204, 52734375, 85766121, 113379904, 466948881, 8031810176, 13051691536, 42618442977, 64339296875, 84835994984, 90075015625, 229783203125, 1785793904896, 5352009260481

Offset

1,1

Comments

Integers k that have exactly two distinct prime factors p_i, p_j with exponents e_i, e_j satisfying i/e_i + j/e_j = 1 where i, j are the 1-based indices of the primes (A000040).

Links

Table of n, a(n) for n=1..23.

Example

For k = 216 = 2^3 * 3^3 we have 1/3 + 2/3 = 1 thus k = 216 is a term.
For k = 941192 = 2^3 * 7^6 we have 1/3 + 4/6 = 1 thus k = 941192 is a term.

Prog

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

Crossrefs

Subsequence of A007774.

Sequence in context: A205191 A204650 A115430 * A278976 A179419 A224549

Adjacent sequences: A387975 A387976 A387977 * A387979 A387980 A387981

Keyword

nonn,more

Author

Ctibor O. Zizka, Oct 13 2025

Status

approved