A372469 -id:A372469 - cp's OEIS frontend

A372468 The number of divisors of the numbers whose number of divisors is a power of 2 (A036537).

1, 2, 2, 2, 4, 2, 4, 4, 2, 2, 4, 4, 2, 2, 4, 4, 2, 8, 4, 4, 2, 8, 2, 4, 4, 4, 2, 4, 4, 8, 2, 8, 2, 4, 2, 4, 2, 8, 4, 8, 4, 4, 2, 2, 4, 4, 8, 2, 4, 8, 2, 2, 4, 4, 8, 2, 4, 2, 4, 4, 4, 8, 2, 4, 4, 4, 4, 2, 2, 8, 2, 8, 8, 4, 2, 2, 8, 4, 2, 8, 4, 4, 4, 16, 4, 4, 4

Offset: 1

Amiram Eldar, May 02 2024

Also, the number of infinitary divisors of the numbers whose number of divisors is a power of 2.

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

Cf. A000005, A036537, A037445, A372469, A372470.

Select[DivisorSigma[0, Range[300]], # == 2^IntegerExponent[#, 2] &]

lista(n) = select(x -> x >> valuation(x, 2) == 1, vector(n, i, numdiv(i)));

a(n) = A000005(A036537(n)).
a(n) = A037445(A036537(n)).
a(n) = A372470(A036537(n)).
a(n) = 2^A372469(n).

A372505 a(n) = log_2(A368473(n)).

Original entry on oeis.org

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

Offset: 1

Amiram Eldar, May 04 2024

The first position of k, for k = 0, 1, ..., is 1, 4, 15, 126, 1134, ..., which is the position of A085629(2^k) in A138302.

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

Cf. A005361, A085629, A138302, A368473.

Cf. A369934, A370078, A372467, A372469.

f[n_] := Module[{p = Times @@ FactorInteger[n][[;; , 2]], e}, e = IntegerExponent[p, 2]; If[p == 2^e, e, Nothing]]; Array[f, 150]

lista(kmax) = {my(p, e); for(k = 1, kmax, p = vecprod(factor(k)[, 2]); e = valuation(p, 2); if(p >> e == 1, print1(e, ", ")));}

a(n) = log_2(A005361(A138302(n))).

cp's OEIS Frontend

A372468 The number of divisors of the numbers whose number of divisors is a power of 2 (A036537).

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