A392031 a(n) is the smallest k which has exactly n divisors d such that sigma(d) = sigma(d + k/d) where sigma = A000203.

1, 14, 120, 4080, 132132, 7361280

Offset

0,2

Links

Table of n, a(n) for n=0..5.

Example

a(1) = 14 because k = 14 has exactly one divisor d = 14 such that sigma(14) = sigma(14 + 14/14) = 24.

Prog

(Magma) [Min([k: k in [1..132132] | #[d: d in Divisors(k) | SumOfDivisors(d) eq SumOfDivisors(d + (k div d))] eq n]): n in [1..4]];
(PARI) isok(k, n) = sumdiv(k, d, sigma(d)==sigma(d+k/d)) == n;
a(n) = my(k=1); while (!isok(k, n), k++); k; \\ Michel Marcus, Jan 04 2026

Crossrefs

Cf. A000005, A000203.

Sequence in context: A004312 A002056 A249980 * A206635 A163942 A206628

Adjacent sequences: A392028 A392029 A392030 * A392032 A392033 A392034

Keyword

nonn,more

Author

Juri-Stepan Gerasimov, Dec 27 2025

Extensions

a(0) = 1 inserted by Michel Marcus, Jan 04 2026

Status

approved