A095402 Sum of digits of all distinct prime factors of n.

0, 2, 3, 2, 5, 5, 7, 2, 3, 7, 2, 5, 4, 9, 8, 2, 8, 5, 10, 7, 10, 4, 5, 5, 5, 6, 3, 9, 11, 10, 4, 2, 5, 10, 12, 5, 10, 12, 7, 7, 5, 12, 7, 4, 8, 7, 11, 5, 7, 7, 11, 6, 8, 5, 7, 9, 13, 13, 14, 10, 7, 6, 10, 2, 9, 7, 13, 10, 8, 14, 8, 5, 10, 12, 8, 12, 9, 9, 16, 7, 3, 7, 11, 12, 13, 9, 14, 4, 17, 10

Offset

1,2

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

n = 1000: prime set = {2, 5}, a[1000] = 7;
n = 255255: prime set={3, 5, 7, 11, 13, 17}, a[255255]= 3+5+7+2+4+8 = 29.

Mathematica

ffi[x_] :=Flatten[FactorInteger[x]] lf[x_] :=Length[FactorInteger[x]] ba[x_] :=Table[Part[ffi[x], 2*j-1], {j, 1, lf[x]}] sd[x_] :=Apply[Plus, IntegerDigits[x]] tdp[x_] :=Flatten[Table[IntegerDigits[Part[ba[x], j]], {j, 1, lf[x]}], 1] sdp[x_] :=Apply[Plus, tdp[x]] Table[sdp[w], {w, 1, 150}]
Table[Total[Flatten[IntegerDigits[First/@FactorInteger[n]]]], {n, 1, 100}] (Zak Seidov)

Prog

(Python)
from sympy import factorint
def a(n): return sum(sum(map(int, str(p))) for p in factorint(n))
print([a(n) for n in range(1, 91)]) # Michael S. Branicky, Dec 12 2023

Crossrefs

Cf. A007953, A051351, A141346.

Sequence in context: A369742 A367476 A141346 * A086294 A361632 A075860

Adjacent sequences: A095399 A095400 A095401 * A095403 A095404 A095405

Keyword

nonn,base

Author

Labos Elemer, Jun 21 2004

Status

approved