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Primes p of the form 1 mod 4 such that p+1 has a prime factor of the form 1 mod 4.
1

%I #23 Mar 13 2020 12:54:07

%S 29,73,89,101,109,149,173,181,193,229,233,269,313,317,337,349,373,389,

%T 409,449,457,509,521,569,577,653,673,677,701,709,769,809,821,829,853,

%U 857,929,941,953,1009,1013,1021,1049,1069,1097,1109,1117,1129,1153,1181

%N Primes p of the form 1 mod 4 such that p+1 has a prime factor of the form 1 mod 4.

%C Vaguely related to odd perfect numbers - they must have one prime 1 mod 4 with an exponent 1 mod 4.

%H Robert Israel, <a href="/A210499/b210499.txt">Table of n, a(n) for n = 1..10000</a>

%e 29 == 1 mod 4 and 29+1 = 30 = 2*3*5 has 5 == 1 mod 4 as a prime factor.

%p filter:= proc(n) isprime(n) and has(1, numtheory:-factorset(n+1) mod 4) end proc:

%p select(filter, [seq(i,i=1..2000,4)]); # _Robert Israel_, Mar 13 2020

%t Select[Prime[Range[500]], Mod[# - 1, 4] == 0 && Sort[Mod[Transpose[FactorInteger[# + 1]][[1]] - 1, 4]][[1]] == 0 &] (* _T. D. Noe_, Jan 25 2013 *)

%Y Cf. A000396, A002144, A016813.

%K nonn

%O 1,1

%A _Jon Perry_, Jan 25 2013