A072592 Even numbers with at least one prime factor of form 4*k+1.

10, 20, 26, 30, 34, 40, 50, 52, 58, 60, 68, 70, 74, 78, 80, 82, 90, 100, 102, 104, 106, 110, 116, 120, 122, 130, 136, 140, 146, 148, 150, 156, 160, 164, 170, 174, 178, 180, 182, 190, 194, 200, 202, 204, 208, 210, 212, 218, 220, 222, 226, 230, 232, 234, 238

Offset: 1

Author

Reinhard Zumkeller, Jun 23 2002

Keywords

• nonn

Comments

Conjecture: this is exactly the sequence whose terms are twice those of A009003. (This has been verified for all terms<=500.) Compare A009003. - John W. Layman, Mar 12 2008

The conjecture is true. See comments on A008846 and A004613. - Lambert Herrgesell (zero815(AT)googlemail.com), Apr 24 2008

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A005843, A002144, A072591, A009003, A008846, A004613.

Programs

Mathematica

opfQ[n_]:=Count[Transpose[FactorInteger[n]][[1]],?(IntegerQ[ (#-1)/4]&)]>0; Select[Range[2,250,2],opfQ] (* _Harvey P. Dale, Jun 02 2012 *)

Python

from itertools import count, islice
from sympy import primefactors
def A072592_gen(startvalue=1): # generator of terms >= startvalue
    return (n<<1 for n in count(max(startvalue,1)) if any(p&3==1 for p in primefactors(n)))
A072592_list = list(islice(A072592_gen(),20)) # Chai Wah Wu, Jul 07 2024

Formula

A072591(a(n)) = 0.