A385430 Least number k such that k and k + n! have the same number of divisors.

2, 3, 5, 5, 7, 7, 11, 23, 17, 11, 17, 29, 46, 19, 43, 23, 31, 37, 89, 29, 31, 31, 97, 62, 41, 59, 47, 67, 159, 107, 127, 79, 37, 97, 61, 131, 86, 43, 97, 53, 61, 97, 71, 47, 94, 101, 233, 53, 83, 61, 249, 53, 71, 158, 71, 149, 107, 134, 254, 206, 166, 131, 271

Offset: 1

Author

Robert G. Wilson v, Jul 31 2025

Keywords

• nonn
• changed

Comments

Inspired by A284783.

First differs from A037153 at n=13 (and when they differ a(n) is a composite < A037153(n)).

Examples

			a(1) = 2 since d(2) = d(3) = 2;
a(5) = 7 since d(7) = d(7+5!) = 2;
a(13) = 46 since d(46) = d(46+13!) = 4; etc.
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..82

Crossrefs

Cf. A000005, A000142, A006881, A037153, A284783.

Programs

Mathematica

a[n_] := Block[{k = 2}, While[ DivisorSigma[0, k] != DivisorSigma[0, k + n!], k++]; k]; Array[ a, 51]

PARI

a(n) = my(k=1); while (numdiv(k) != numdiv(k+n!), k++); k; \\ Michel Marcus, Aug 02 2025

Extensions

More terms from Sean A. Irvine, Aug 08 2025