A334455 a(n) is unique integer k such that sigma(A051281(n)) = tau(A051281(n))^k (where sigma is the sum of divisors (A000203) and tau the number of divisors (A000005)), with a(1) = 1.

1, 2, 3, 5, 7, 4, 5, 4, 6, 13, 5, 8, 17, 6, 9, 19, 10, 10, 7, 11, 11, 8, 8, 12, 12, 13, 9, 9, 7, 6, 15, 31, 8, 16, 11, 17, 12, 18, 18, 19, 13, 13, 13, 8, 10, 10, 11, 11, 22, 9, 12, 24, 10, 25, 17, 17, 13, 13, 14, 14, 14, 19, 12, 12, 15, 15, 61, 21, 16, 32, 13

Offset: 1

Author

Rémy Sigrist, Nov 10 2020

Keywords

• nonn

Examples

			For n = 7:
- A051281(7) = 889,
- sigma(889) = 1024,
- tau(889) = 4,
- 1024 = 4^5,
- so a(7) = 5.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..12885
• Rémy Sigrist, Colored scatterplot of the first 12885 terms (where the color is function of tau(A051281(n)))
• Rémy Sigrist, PARI program for A334455

Crossrefs

Cf. A000005, A000203, A051281, A225369.

Programs

PARI

See Links section.

Formula

a(n) = log(A000203(A051281(n))) / log(A000005(A051281(n))) for n > 1.