

A268379


Numbers having more prime factors of the form 4*k+1 than of the form 4*k+3, when counted with multiplicity.


4



5, 10, 13, 17, 20, 25, 26, 29, 34, 37, 40, 41, 50, 52, 53, 58, 61, 65, 68, 73, 74, 75, 80, 82, 85, 89, 97, 100, 101, 104, 106, 109, 113, 116, 122, 125, 130, 136, 137, 145, 146, 148, 149, 150, 157, 160, 164, 169, 170, 173, 175, 178, 181, 185, 193, 194, 195, 197, 200, 202, 205, 208, 212, 218, 221
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OFFSET

1,1


COMMENTS

Numbers n for which A083025(n) > A065339(n) or equally, for which A079635(n) > 0.
Closed under multiplication.


LINKS

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


EXAMPLE

75 = 3*5*5 is included as there are more prime factors of the form 4k+1 (here two 5's) than of the form 4k+3 (here just one 3).


MATHEMATICA

Rest@ Position[Array[Map[Length, {Select[#, Mod[#, 4] == 1 &], Select[#, Mod[#, 4] == 3 &]}] &@ Flatten@ Apply[Table[#1, {#2}] &, FactorInteger@ #, 1] &, {221}], {a_, b_} /; a > b] // Flatten (* Michael De Vlieger, Feb 05 2016 *)


PROG

(Scheme, with Antti Karttunen's IntSeqlibrary)
(define A268379 (MATCHINGPOS 1 1 (lambda (n) (> (A083025 n) (A065339 n)))))
(define A268379 (MATCHINGPOS 1 1 (COMPOSE positive? A079635)))
(PARI) isok(n) = {my(f = factor(n), nb1 = 0, nb3 = 0); for (i=1, #f~, m = f[i, 1] % 4; if (m == 1, nb1 += f[i, 2], if (m == 3, nb3 += f[i, 2])); ); return (nb1 > nb3); } \\ Michel Marcus, Feb 04 2016


CROSSREFS

Cf. A065339, A079635, A083025.
Cf. also A001481, A072202, A268380.
Subsequence of A268381.
Differs from A221265 for the first time at n=22, as here a(22) = 75, a value missing from A221265.
Sequence in context: A024507 A004431 A025302 * A221265 A055096 A313386
Adjacent sequences: A268376 A268377 A268378 * A268380 A268381 A268382


KEYWORD

nonn


AUTHOR

Antti Karttunen, Feb 03 2016


STATUS

approved



