A268380 - OEIS

A268380

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

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

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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

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