

A268380


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


4



3, 6, 7, 9, 11, 12, 14, 18, 19, 21, 22, 23, 24, 27, 28, 31, 33, 36, 38, 42, 43, 44, 45, 46, 47, 48, 49, 54, 56, 57, 59, 62, 63, 66, 67, 69, 71, 72, 76, 77, 79, 81, 83, 84, 86, 88, 90, 92, 93, 94, 96, 98, 99, 103, 105, 107, 108, 112, 114, 117, 118, 121, 124, 126, 127, 129, 131, 132, 133, 134, 135, 138, 139, 141
(list;
graph;
refs;
listen;
history;
text;
internal format)



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

45 = 3*3*5 is included as there are more prime factors of the form 4k+3 (here two 3's) than prime factors of the form 4k+1 (here just one 5).


MATHEMATICA

Position[Array[Map[Length, {Select[#, Mod[#, 4] == 1 &], Select[#, Mod[#, 4] == 3 &]}] &@ Flatten@ Apply[Table[#1, {#2}] &, FactorInteger@ #, 1] &, {141}], {a_, b_} /; a < b] // Flatten (* Michael De Vlieger, Feb 05 2016 *)


PROG

(Scheme, with Antti Karttunen's IntSeqlibrary)
(define A268380 (MATCHINGPOS 1 1 (lambda (n) (< (A083025 n) (A065339 n)))))
(PARI) isok(n) = {my(f = factor(n)); sum(k=1, #f~, ((f[k, 1] % 4)==1)*f[k, 2]) < sum(k=1, #f~, ((f[k, 1] % 4)==3)*f[k, 2]); } \\ Michel Marcus, Feb 05 2016


CROSSREFS

Complement: A268381.
Cf. A079635, A065339, A083025.
Cf. also A072202, A268379.
Differs from A221264 for the first time at n=23, where a(23) = 45, a value missing from A221264.
Sequence in context: A324696 A186348 A071822 * A268378 A221264 A026415
Adjacent sequences: A268377 A268378 A268379 * A268381 A268382 A268383


KEYWORD

nonn


AUTHOR

Antti Karttunen, Feb 05 2016


STATUS

approved



