A373968 - OEIS

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A373968

a(n) is the number of divisors of n that are Duffinian numbers (A003624).

0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, 0, 3, 0, 1, 0, 1, 1, 0, 0, 2, 1, 0, 2, 1, 0, 0, 0, 4, 0, 0, 1, 3, 0, 0, 1, 2, 0, 1, 0, 1, 1, 0, 0, 3, 1, 2, 0, 1, 0, 2, 1, 2, 1, 0, 0, 1, 0, 0, 3, 5, 1, 0, 0, 1, 0, 1, 0, 4, 0, 0, 2, 1, 1, 1, 0, 3, 3, 0, 0, 2, 1, 0, 0, 2

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,8

LINKS

Table of n, a(n) for n=1..88.

FORMULA

a(p^k)) = k - 1, for p prime and k >= 1.

EXAMPLE

Since A003624(1) = 4 then a(1) = a(2) = a(3) = 0 and a(4) = 1.

a(8) = 2 because 8 has the divisors 4 = A003624(1) and 8 = A003624(2).

MATHEMATICA

a[n_] := DivisorSum[n, 1 &, CompositeQ[#] && CoprimeQ[#, DivisorSigma[1, #]] &]; Array[a, 100] (* Amiram Eldar, Jul 19 2024 *)