A392367 Numbers whose greatest prime factor is a Fermat prime.

3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 24, 25, 27, 30, 34, 36, 40, 45, 48, 50, 51, 54, 60, 68, 72, 75, 80, 81, 85, 90, 96, 100, 102, 108, 119, 120, 125, 135, 136, 144, 150, 153, 160, 162, 170, 180, 187, 192, 200, 204, 216, 221, 225, 238, 240, 243, 250, 255, 257, 270

Offset

1,1

Comments

A143513 \ {1} is a subsequence that does not include the terms 119, 187, 221, 238, 357, 374, 442, 476, 561, 595, ... .

Numbers k such that A006530(k) is in A019434.

Links

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

Formula

Sum_{n>=1} 1/a(n) = Sum_{q in A019434} (1/q) * Product_{primes p <= q} p/(p-1) = 2.11507281179419933506... . If there are only 5 Fermat primes, then this sum is a rational number: 2.6569019...*10^23656 / 1.2561751...*10^23656.

Mathematica

fermatQ[p_] := OddQ[p] && p == 2^IntegerExponent[p-1, 2] + 1;
Select[Range[300], fermatQ[FactorInteger[#][[-1, 1]]] &]

Prog

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

Crossrefs

Cf. A006530, A019434, A143512, A143513, A392368.

Sequence in context: A080307 A001969 A075311 * A032786 A080309 A281746

Adjacent sequences: A392364 A392365 A392366 * A392368 A392369 A392370

Keyword

nonn,easy

Author

Amiram Eldar, Jan 09 2026

Status

approved