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 A070314 #15 Apr 24 2025 01:32:58 %S A070314 0,-1,-2,4,-12,0,90,28,404,250,329850,39916118,2834088,75021616, %T A070314 3790360374,46271010,993974,956666,123610842,1713311273189068, %U A070314 117876621366,2703875810364,93799610095767534,148139754734068388,765041185860961083618,38681321803817920155550 %N A070314 a(n) = P(n!+1)-P(2^n+1) where P(x) is the largest prime factor in x. %C A070314 Is it always true that a(n) > 0 for n > 5? More generally, if m is an integer > 2, is there always an integer f(m) such that P(n!+1) > P(m^n+1) for n > f(m) (it seems that f(2) = 5, f(3) = 7, f(4) = 17, ...). %H A070314 Amiram Eldar, <a href="/A070314/b070314.txt">Table of n, a(n) for n = 0..139</a> %F A070314 a(n) = A002583(n) - A002587(n). - _Amiram Eldar_, Apr 23 2025 %t A070314 gpf[n_] := FactorInteger[n][[-1,1]]; a[n_] := gpf[n!+1] - gpf[2^n+1]; Array[a, 26, 0] (* _Amiram Eldar_, Apr 23 2025 *) %Y A070314 Cf. A002583, A002587, A006530. %K A070314 sign %O A070314 0,3 %A A070314 _Benoit Cloitre_, May 12 2002 %E A070314 Offset changed to 0 and a(0) prepended by _Amiram Eldar_, Apr 23 2025