A358879 - OEIS

%I #7 Dec 04 2022 20:24:31

%S 2917,5443,7187,9133,10357,12227,12967,13043,14243,17047,20507,20743,

%T 21767,25657,27893,27997,28163,30307,32323,32443,33493,33623,34157,

%U 34367,34897,35537,37783,37957,39827,41387,41893,42793,43633,44357,49109,49993,56597,56857

%N Primes p such that p^2 + 1 has more divisors than p^2 - 1.

%C Fewer than 1.2% of the first million primes have this property.

%C For all primes p > 3, p^2 - 1 is divisible by 24 (since it is factorable as (p-1)*(p+1)), but p^2 + 1, although it is even, is divisible by neither 4 nor 3.

%e 2917 is a term:

%e 2917^2 - 1 = 8508888 = 2^3 * 3^6 * 1459 has 56 divisors, but

%e 2917^2 + 1 = 8508890 = 2 * 5 * 13 * 29 * 37 * 61 has 64.

%e 399173 is a term:

%e 399173^2 - 1 = 159339083928 = 2^3 * 3 * 66529 * 99793 has 32 divisors, but

%e 399173^2 + 1 = 159339083930 = 2 * 5 * 13 * 17 * 29 * 53 * 61 * 769 has 256.

%Y Cf. A000005, A000040, A341655, A341658, A341660.

%K nonn

%O 1,1

%A _Jon E. Schoenfield_, Dec 04 2022