A392368 Numbers whose least prime factor is a Fermat prime.

3, 5, 9, 15, 17, 21, 25, 27, 33, 35, 39, 45, 51, 55, 57, 63, 65, 69, 75, 81, 85, 87, 93, 95, 99, 105, 111, 115, 117, 123, 125, 129, 135, 141, 145, 147, 153, 155, 159, 165, 171, 175, 177, 183, 185, 189, 195, 201, 205, 207, 213, 215, 219, 225, 231, 235, 237, 243

Offset

1,1

Comments

Differs from A086748 by having terms like 17, 257, 289, 323, 391, and 493. Is A086748 a subsequence of this sequence?

Numbers k such that A020639(k) is in A019434.

The asymptotic density of this sequence is Sum_{q in A019434} (1/q) * Product_{primes p < q} (1 - 1/p) = 0.24500742018276270264... . If there are only 5 Fermat primes, then this density is a rational number: 2.7462024...*10^23743 / 1.1208650...*10^23744.

Links

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

Mathematica

fermatQ[p_] := OddQ[p] && p == 2^IntegerExponent[p-1, 2] + 1;
Select[Range[250], fermatQ[FactorInteger[#][[1, 1]]] &]

Prog

(PARI) isfermat(p) = p % 2 && p == 1 << valuation(p-1, 2) + 1;
isok(k) = k > 1 && isfermat(vecmin(factor(k)[, 1]));

Crossrefs

Cf. A019434, A020639, A086748, A143512, A143513, A392367.

Sequence in context: A120695 A355898 A103578 * A116649 A129771 A209837

Adjacent sequences: A392365 A392366 A392367 * A392369 A392370 A392371

Keyword

nonn,easy

Author

Amiram Eldar, Jan 09 2026

Status

approved