A268377 Numbers n such that any prime factor of the form 4k+1 has even multiplicity.

1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 14, 16, 18, 19, 21, 22, 23, 24, 25, 27, 28, 31, 32, 33, 36, 38, 42, 43, 44, 46, 47, 48, 49, 50, 54, 56, 57, 59, 62, 63, 64, 66, 67, 69, 71, 72, 75, 76, 77, 79, 81, 83, 84, 86, 88, 92, 93, 94, 96, 98, 99, 100, 103, 107, 108, 112, 114, 118, 121, 124, 126, 127, 128, 129, 131, 132, 133

Offset

1,2

Comments

Closed under multiplication.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Example

Neither 5 or 10 (= 2*5) are included, because the prime factor 5 (of the form 4k+1) occurs just once.
6 = 2*3 is present, as there are no prime factors of 4k+1 present at all, and zero is an even number.
Also 25 (5*5) and 50 (2*5*5) and 75 (3*5*5) and 625 (5*5*5*5) are included, because in all of them, the prime factor 5 (of the form 4k+1) occurs an even number of times.

Mathematica

{1}~Join~Select[Range@ 140, NoneTrue[FactorInteger@ #, And[Mod[First@ #, 4] == 1, OddQ@ Last@ #] &] &] (* Michael De Vlieger, Feb 04 2016, Version 10 *)

Prog

(Scheme) (define A268377 (MATCHING-POS 1 1 (COMPOSE even? A267113)))
(PARI) isok(n) = {my(f = factor(n)); for (i=1, #f~, if (((f[i, 1] % 4) == 1) && (f[i, 2] % 2), return (0)); ); return (1); } \\ Michel Marcus, Feb 04 2016

Crossrefs

Cf. A267113.

Cf. A268378 (a subsequence).

Cf. A001481, A267099.

Sequence in context: A013939 A343109 A209921 * A201010 A004144 A356930

Adjacent sequences: A268374 A268375 A268376 * A268378 A268379 A268380

Keyword

nonn

Author

Antti Karttunen, Feb 03 2016

Status

approved