A381202 a(n) is the sum of the elements of the set of bases and exponents (including exponents = 1) in the prime factorization of n.

0, 3, 4, 2, 6, 6, 8, 5, 5, 8, 12, 6, 14, 10, 9, 6, 18, 6, 20, 8, 11, 14, 24, 6, 7, 16, 3, 10, 30, 11, 32, 7, 15, 20, 13, 5, 38, 22, 17, 11, 42, 13, 44, 14, 11, 26, 48, 10, 9, 8, 21, 16, 54, 6, 17, 13, 23, 32, 60, 11, 62, 34, 13, 8, 19, 17, 68, 20, 27, 15, 72, 5

Offset: 1

Author

Paolo Xausa, Feb 16 2025

Keywords

• nonn
• easy

Comments

The prime factorization of 1 is the empty set, so a(1) = 0 by convention (empty sum).

Examples

			a(12) = 6 because 12 = 2^2*3^1, the set of these bases and exponents is {1, 2, 3} and 1 + 2 + 3 = 6.
a(31500) = 18 because 31500 = 2^2*3^2*5^3*7^1, the set of these bases and exponents is {1, 2, 3, 5, 7} and 1 + 2 + 3 + 5 + 7 = 18.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A008474, A338038, A381201, A381203, A381204, A381205.

Programs

Mathematica

A381202[n_] := If[n == 1, 0, Total[Union[Flatten[FactorInteger[n]]]]];
Array[A381202, 100]

PARI

a(n) = my(f=factor(n)); vecsum(setunion(Set(f[,1]), Set(f[,2]))); \\ Michel Marcus, Feb 18 2025