A366074 - OEIS

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A366074

The number of "Fermi-Dirac primes" (A050376) that are unitary divisors of n.

0, 1, 1, 1, 1, 2, 1, 0, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 0, 2, 1, 3, 1, 0, 2, 2, 2, 2, 1, 2, 2, 1, 1, 3, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 1, 2, 1, 2, 2, 1, 3, 1, 2, 2, 0, 2, 3, 1, 2, 2, 3, 1, 1, 1, 2, 2, 2, 2, 3, 1, 2, 1, 2, 1, 3, 2, 2, 2

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OFFSET

1,6

COMMENTS

First differs from A293439 at n = 128.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Unitary Divisor.

FORMULA

Additive with a(p^e) = A209229(e).

Sum_{k=1..n} a(k) ~ n * (log(log(n)) + B + C), where B is Mertens's constant (A077761) and C = -P(2) + Sum_{k>=1} (P(2^k) - P(2^k+1)) = -0.13145993422430119364..., where P(s) is the prime zeta function.

MATHEMATICA

f[p_, e_] := If[e == 2^IntegerExponent[e, 2], 1, 0]; a[1] = 0; a[n_] := Plus @@ f @@@ FactorInteger[n]; Array[a, 100]

PROG

(PARI) a(n) = vecsum(apply(x -> (x == 1 << valuation(x, 2)), factor(n)[, 2]));

CROSSREFS

Cf. A050376, A064547, A077610, A077761, A209229, A366073.

Sequence in context: A335451 A366078 A344652 * A293439 A144095 A362719

Adjacent sequences: A366071 A366072 A366073 * A366075 A366076 A366077

KEYWORD

nonn,easy

AUTHOR

Amiram Eldar, Sep 28 2023

STATUS

approved