A387394 Total number of 2's in the decimal digits of the divisors of n.
0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 1, 3, 1, 3, 1, 2, 1, 2, 1, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 2, 0, 3, 0, 3, 0, 2, 0, 3, 0, 2, 0, 3, 0, 2, 0, 2, 0, 2, 0, 3, 0, 2, 1, 2, 0, 3, 0, 1, 1, 1, 0, 4, 0, 1, 1, 1, 0, 2, 0, 2, 1, 2, 0, 5, 0, 1, 1, 3, 0, 1, 0, 3, 0, 1, 0, 4, 0, 1, 0
Offset: 1
Examples
a(22) = 3 because among the divisors of 22, 2 has one 2 and 22 has two, for a total of 3.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Maple
f:= proc(n) local d; add(numboccur(2, convert(d, base, 10)), d=numtheory:-divisors(n)) end proc: map(f, [$1..200]);
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Mathematica
a[n_]:=Count[IntegerDigits[Divisors[n]]//Flatten, 2]; Array[a, 99] (* Stefano Spezia, Aug 29 2025 *)
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PARI
a(n) = sumdiv(n, d, #select(x->(x==2), digits(d))); \\ Michel Marcus, Aug 28 2025
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Python
from sympy import divisors def a(n): return sum(str(d).count("2") for d in divisors(n, generator=True)) print([a(n) for n in range(1, 100)]) # Michael S. Branicky, Aug 29 2025