A366308 The number of infinitary divisors of n that are terms of A366242.

1, 2, 2, 1, 2, 4, 2, 2, 1, 4, 2, 2, 2, 4, 4, 2, 2, 2, 2, 2, 4, 4, 2, 4, 1, 4, 2, 2, 2, 8, 2, 4, 4, 4, 4, 1, 2, 4, 4, 4, 2, 8, 2, 2, 2, 4, 2, 4, 1, 2, 4, 2, 2, 4, 4, 4, 4, 4, 2, 4, 2, 4, 2, 2, 4, 8, 2, 2, 4, 8, 2, 2, 2, 4, 2, 2, 4, 8, 2, 4, 2, 4, 2, 4, 4, 4, 4

Offset

1,2

Links

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

Formula

Multiplicative with a(p^e) = 2^A139351(e).

a(n) = 2^A366246(n).

a(n) = A037445(n)/A366309(n).

a(n) = A037445(A366244(n)).

a(n) >= 1, with equality if and only if n is in A366243.

a(n) <= A037445(n), with equality if and only if n is in A366242.

Mathematica

s[0] = 0; s[n_] := s[n] = s[Floor[n/4]] + If[OddQ[Mod[n, 4]], 1, 0]; f[p_, e_] := 2^s[e]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

Prog

(PARI) s(e) = if(e > 3, s(e\4)) + e%2 \\ after Charles R Greathouse IV at A139351
a(n) = vecprod(apply(x -> 2^s(x), factor(n)[, 2]));

Crossrefs

Cf. A037445, A139351, A366242, A366243, A366244, A366246, A366309.

Sequence in context: A055076 A069780 A369307 * A347089 A354825 A210531

Adjacent sequences: A366305 A366306 A366307 * A366309 A366310 A366311

Keyword

nonn,easy,mult

Author

Amiram Eldar, Oct 06 2023

Status

approved