A134599 - OEIS

A134599

Sum of digital sums (base 3) of the prime factors of n.

0, 2, 1, 4, 3, 3, 3, 6, 2, 5, 3, 5, 3, 5, 4, 8, 5, 4, 3, 7, 4, 5, 5, 7, 6, 5, 3, 7, 3, 6, 3, 10, 4, 7, 6, 6, 3, 5, 4, 9, 5, 6, 5, 7, 5, 7, 5, 9, 6, 8, 6, 7, 7, 5, 6, 9, 4, 5, 5, 8, 5, 5, 5, 12, 6, 6, 5, 9, 6, 8, 7, 8, 5, 5, 7, 7, 6, 6, 7, 11, 4, 7, 3, 8, 8, 7, 4, 9, 5, 7, 6, 9, 4, 7, 6, 11, 5, 8, 5, 10, 5, 8, 5, 9, 7

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OFFSET

1,2

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

FORMULA

If p_1*p_2*p_3* ... *p_m = n is the unique prime factorization of n, then a(n) = Sum_{k=1..m} ds_3(p_k), where ds_3 is the digital sum base 3.

Totally additive with a(p) = A053735(p). - Amiram Eldar, Jul 30 2025

EXAMPLE

a(6) = 3, since 6 = 2*3 and so a(6) = ds_3(2) + ds_3(3) = 2 + 1.

MATHEMATICA

f[p_, e_] := e * DigitSum[p, 3]; a[1] = 0; a[n_] := Plus @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Jul 30 2025 *)