A392047 Positive integers whose canonical prime factorization p_1^e_1*...*p_r^e_r satisfies that {p_1, ..., p_r, e_1, ..., e_r} is a set of 2*r consecutive integers.

2, 8, 9, 48, 81, 162, 625, 2000, 2025, 2592, 3888, 5000, 5625, 15625, 25920, 58320, 117649, 120000, 455625, 750000, 911250, 1265625, 2531250, 5764801, 13720000, 19208000, 22325625, 37340352, 37515625, 43758225, 56010528, 58320000, 62015625, 73530625, 85750000, 87127488

Offset

1,1

Links

Felix Huber, Table of n, a(n) for n = 1..1142

Example

162 = 2^1*3^4 is a term since 1, 2, 3, 4 are consecutive integers.
22325625 = 3^6*5^4*7^2 is a term since 2, 3, 4, 5, 6, 7 are consecutive integers.

Maple

A392047List := N -> sort([op(A392045List(N)), op(A392046List(N))]): A392047List(235298000);

Prog

(PARI) isok(k) = my(f=factor(k), v=vecsort(concat(f[, 1], f[, 2]), , 8)); #v && (#v == 2*#f~) && (vecmax(v) - vecmin(v) == #v-1); \\ Michel Marcus, Jan 09 2026

Crossrefs

Cf. A111774, A382330, A390784.

Union of A392045 and A392046.

Cf. A097320, A383397, A387172, A387586, A389339, A389340, A389795.

Sequence in context: A381215 A181476 A055678 * A301281 A091793 A350454

Adjacent sequences: A392044 A392045 A392046 * A392048 A392049 A392050

Keyword

nonn,easy

Author

Felix Huber, Jan 05 2026

Status

approved