This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A341665 #11 Mar 04 2021 01:42:42 %S A341665 7,23,83,227,263,359,479,503,563,1187,2999,3803,4703,4787,4919,5939, %T A341665 6599,8819,10667,14159,16139,16187,18119,21227,22943,25847,26003, %U A341665 26903,27827,29123,29339,29663,36263,43403,44519,44963,46199,47123,48947,49103,49499 %N A341665 Primes p such that p^5 - 1 has 8 divisors. %C A341665 For each term p, p^5 - 1 = (p-1)*(p^4 + p^3 + p^2 + p + 1) is a number of the form 2*q*r (where q and r are distinct primes): p-1 = 2*q and p^4 + p^3 + p^2 + p + 1 = r. %C A341665 Conjecture: sequence is infinite. %e A341665 p = factorization %e A341665 n a(n) p^5 - 1 of (p^5 - 1) %e A341665 - ---- -------------- --------------------- %e A341665 1 7 16806 2 * 3 * 2801 %e A341665 2 23 6436342 2 * 11 * 292561 %e A341665 3 83 3939040642 2 * 41 * 48037081 %e A341665 4 227 602738989906 2 * 113 * 2666986681 %e A341665 5 263 1258284197542 2 * 131 * 4802611441 %e A341665 6 359 5963102065798 2 * 179 * 16656709681 %e A341665 7 479 25216079618398 2 * 239 * 52753304641 %e A341665 8 503 32198817702742 2 * 251 * 64141071121 %e A341665 ... %t A341665 Select[Range[50000], PrimeQ[#] && DivisorSigma[0, #^5 - 1] == 8 &] (* _Amiram Eldar_, Feb 26 2021 *) %o A341665 (PARI) isok(p) = isprime(p) && (numdiv(p^5-1) == 8); \\ _Michel Marcus_, Feb 26 2021 %Y A341665 Cf. A000005, A000040, A309906, A341664. %K A341665 nonn %O A341665 1,1 %A A341665 _Jon E. Schoenfield_, Feb 26 2021