A141346 Sum of the distinct digits of the prime factors of n.

0, 2, 3, 2, 5, 5, 7, 2, 3, 7, 1, 5, 4, 9, 8, 2, 8, 5, 10, 7, 10, 3, 5, 5, 5, 6, 3, 9, 11, 10, 4, 2, 4, 10, 12, 5, 10, 12, 4, 7, 5, 12, 7, 3, 8, 5, 11, 5, 7, 7, 11, 6, 8, 5, 6, 9, 13, 11, 14, 10, 7, 6, 10, 2, 9, 6, 13, 10, 5, 14, 8, 5, 10, 12, 8, 12, 8, 6, 16, 7, 3, 7, 11, 12, 13, 9, 14, 3, 17, 10

Offset

1,2

Comments

Motivated by seeking an explanation for A080592. For n >= 2, 1 <= a(n) <= 45. For n >= 1, a(n) <= A095402(n).

Links

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

Example

a(44) = 3 as 44 = 2^2 * 11 and the sum of the distinct digits of the prime factors is 1 + 2 (whereas A095402(44) = 4 = 1 + 1 + 2).

Mathematica

Join[{0}, Rest[Total[Union[Flatten[IntegerDigits/@Transpose[ FactorInteger[ #]][[1]]]]]&/@Range[90]]] (* Harvey P. Dale, Nov 30 2011 *)

Prog

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

Crossrefs

Cf. A095402, A080592, A008472.

Sequence in context: A137851 A369742 A367476 * A095402 A086294 A361632

Adjacent sequences: A141343 A141344 A141345 * A141347 A141348 A141349

Keyword

base,nonn

Author

Rick L. Shepherd, Jun 26 2008

Status

approved