A080773 -id:A080773 - cp's OEIS frontend

A134598 Duplicate of A080773.

1, 2, 2, 2, 3, 3, 3, 4, 3, 3, 4, 3, 4, 4, 4, 2, 5, 3, 4, 5, 4, 4, 5, 4, 4, 6, 5, 4, 5, 5, 5, 5, 3, 5, 6, 3, 4, 5, 5, 3, 6, 4, 5, 6, 5, 5, 6, 6, 5, 4, 5, 4, 7, 5, 6, 5, 5, 5, 6, 5, 6, 7, 6, 5, 6, 3, 4, 6, 6, 4, 7, 3, 4, 6, 5, 6, 6, 5, 6, 8, 4, 4, 7, 4, 5, 6, 6, 4, 7, 6, 6, 7, 6, 5, 7, 3, 7, 7, 6, 4, 5, 5, 6, 7, 5

Offset: 2

Hieronymus Fischer, Nov 11 2007

dead

			a(6)=3, since 6=2*3 and so a(6)=ds_2(2)+ds_2(3)=1+2.

If p_1*p_2*p_3* ... *p_m=n is the unique prime factorization of n, then a(n)=sum{1<=k<=m, ds_2(p_k)}, where ds_2 is the digital sum base 2.

A134599 Sum of digital sums (base 3) of the prime factors of n.

Original entry on oeis.org

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

Offset: 1

Hieronymus Fischer, Nov 11 2007

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

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

Cf. A053735, A080773 (base 2), A118503.

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

a(n) = {my(f = factor(n)); sum(i = 1, #f~, f[i, 2] * sumdigits(f[i, 1], 3));} \\ Amiram Eldar, Jul 30 2025

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

a(1) = 0 prepended by Amiram Eldar, Jul 30 2025

cp's OEIS Frontend

A134598 Duplicate of A080773.

Views

Author

Keywords

Examples

Formula

A134599 Sum of digital sums (base 3) of the prime factors of n.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions