login
A141346
Sum of the distinct digits of the prime factors of n.
3
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
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
KEYWORD
base,nonn
AUTHOR
Rick L. Shepherd, Jun 26 2008
STATUS
approved