A391646 a(n) is the least integer k such that the sum of the prime divisors of k, each taken modulo its exponent in the prime factorization of k, equals n.

1, 9, 8, 72, 1000, 648, 16200, 81000, 1125000, 38896200, 10125000, 496125000, 3735591048, 24310125000

Offset

0,2

Comments

From David A. Corneth, Dec 15 2025: (Start)

a(14) <= 466948881000, a(15) <= 6485401125000, a(17) <= 58368610125000, a(18) <= 7062601825125000.

For any prime p the multiplicity of p in a(n) is at most p+1.

The sequence is well defined via A000586 and inspection for values k where A000586(k) = 0. (End)

a(16) <= 355924540125000.

The least integer k such that A392814(k) = n. - Amiram Eldar, Jan 24 2026

Links

Table of n, a(n) for n=0..13.

Formula

n < A001222(a(n)). - David A. Corneth, Dec 15 2025

Example

a(1) = 9, because 9 = 3^2 and 3 mod 2 = 1.
a(2) = 8, because 8 = 2^3 and 2 mod 3 = 2.
a(3) = 72, because 72 = 2^3 * 3^2 and 2 mod 3 + 3 mod 2 = 3.
a(4) = 1000, because 1000 = 2^3 * 5^3 and 2 mod 3 + 5 mod 3 = 4.
a(5) = 648, because 648 = 2^3 * 3^4 and 2 mod 3 + 3 mod 4 = 5;
and no smaller numbers have these properties.

Prog

(PARI) isok(n, k) = my(f=factor(k)); sum(i=1, #f~, f[i, 1] % f[i, 2]) == n;
a(n) = my(k=2); while (!isok(n, k), k++); k; \\ Michel Marcus, Dec 15 2025

Crossrefs

Cf. A000586, A001222, A001694, A008474, A343923, A392814.

Sequence in context: A253090 A154226 A177187 * A030027 A082201 A357880

Adjacent sequences: A391643 A391644 A391645 * A391647 A391648 A391649

Keyword

nonn,more

Author

Jean-Marc Rebert, Dec 15 2025

Extensions

Incorrect formula removed by Amiram Eldar, Jan 24 2026

Status

approved