A004625 Numbers divisible only by primes congruent to 1 mod 8.

1, 17, 41, 73, 89, 97, 113, 137, 193, 233, 241, 257, 281, 289, 313, 337, 353, 401, 409, 433, 449, 457, 521, 569, 577, 593, 601, 617, 641, 673, 697, 761, 769, 809, 857, 881, 929, 937, 953, 977, 1009, 1033, 1049

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Programs

Magma

[n: n in [1..2000] | forall{d: d in PrimeDivisors(n) | d mod 8 eq 1}]; // Vincenzo Librandi, Aug 20 2012

Mathematica

ok[n_] := And @@ (#1[[2]] == 1 && Mod[#1[[1]], 8] == 1 & ) /@ FactorInteger[n]; Select[ Range[2000], ok] (* Jean-François Alcover, Mar 09 2012 *)

PARI

is(n)=is(n%8!=1, return(0)); my(f=factor(n)[,1]); for(i=1,#f~, if(f[i]%8!=1, return(0))); 1 \\ Charles R Greathouse IV, Jul 02 2016

Extensions

Offset changed from 0 to 1 by Vincenzo Librandi, Aug 20 2012