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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 IntSeq-library)

(define A268380 (MATCHING-POS 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

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Last modified April 20 08:50 EDT 2019. Contains 322306 sequences. (Running on oeis4.)