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

1,2

Comments

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

Links

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A207376 A213197 A378127 * A049277 A214917 A260316

Adjacent sequences: A381199 A381200 A381201 * A381203 A381204 A381205

Keyword

nonn,easy

Author

Paolo Xausa, Feb 16 2025

Status

approved