A302777 - OEIS

A302777

a(n) = 1 if n is of the form p^(2^k) where p is prime and k >= 0, otherwise 0.

0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1

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OFFSET

COMMENTS

Characteristic function of "Fermi-Dirac primes", A050376.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions

FORMULA

a(n) = A209229(A100995(n)).

MATHEMATICA

a[n_] := Boole[n > 1 && Length[(f = FactorInteger[n])] == 1 && (e = f[[;; , 2]]) == 2^IntegerExponent[e, 2]]; Array[a, 100] (* Amiram Eldar, Nov 27 2020 *)

PROG

(PARI)

A209229(n) = (n && !bitand(n, n-1));

A302777(n) = A209229(isprimepower(n));

for(n=1, 121, print1(A302777(n), ", "));

CROSSREFS

Cf. A010051, A069513, A050376, A100995, A209229, A302778 (partial sums).

Sequence in context: A285274 A189081 A296084 * A324828 A332823 A354817

Adjacent sequences: A302774 A302775 A302776 * A302778 A302779 A302780

KEYWORD

nonn

AUTHOR

Antti Karttunen, Apr 16 2018

STATUS

approved