A268379 - OEIS

A268379

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

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 IntSeq-library)

(define A268379 (MATCHING-POS 1 1 (lambda (n) (> (A083025 n) (A065339 n)))))

(define A268379 (MATCHING-POS 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

(Python)

from itertools import count, islice

from sympy import factorint

def A268379_gen(): # generator of terms

return filter(lambda n:sum((f:=factorint(n)).values())-f.get(2, 0) < 2*sum(f[p] for p in f if p & 3 == 1), count(1))

A268379_list = list(islice(A268379_gen(), 30)) # Chai Wah Wu, Jun 28 2022

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