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
Keywords
Examples
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.
Links
- Antti Karttunen, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
{1}~Join~Select[Range@ 140, NoneTrue[FactorInteger@ #, And[Mod[First@ #, 4] == 1, OddQ@ Last@ #] &] &] (* Michael De Vlieger, Feb 04 2016, Version 10 *) -
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 -
Scheme
(define A268377 (MATCHING-POS 1 1 (COMPOSE even? A267113)))
Comments