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A268377 Numbers n such that any prime factor of the form 4k+1 has even multiplicity. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A050126 A013939 A209921 * A201010 A004144 A124391

Adjacent sequences:  A268374 A268375 A268376 * A268378 A268379 A268380

KEYWORD

nonn

AUTHOR

Antti Karttunen, Feb 03 2016

STATUS

approved

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Last modified October 16 15:51 EDT 2019. Contains 328101 sequences. (Running on oeis4.)