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 A387419 #7 Sep 01 2025 11:24:08
%S A387419 1,3,4,7,15,31,40,63,127,255,511,639,1023,2047,2175,2431,4095,5247,
%T A387419 8191,14335,16383,32767,40959,44031,57855,65535,90111,131071,204799,
%U A387419 262143,376831,524287,923647,1048575,1632255,2056191,2097151,2621439,2744319,4194303,6815743,8388607,8781823,16777215,19922943,24068095
%N A387419 Numbers k such that the odd part of (1+k) divides (1 + odd part of A003959(k)), where A003959 is multiplicative with a(p^e) = (p+1)^e.
%C A387419 Like in many sequences of this type, the criterion seems to strongly select for numbers with a long tail of trailing 1-bits. Terms 1, 4 and 40 are probably the only terms that are not in A004767.
%o A387419 (PARI)
%o A387419 A000265(n) = (n>>valuation(n,2));
%o A387419 A003959(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]++); factorback(f); };
%o A387419 isA387419(n) = !((1+A000265(A003959(n)))%A000265(1+n));
%Y A387419 Cf. A000225 (subsequence), A000265, A003959, A004767.
%Y A387419 For similar sequences, see A336700, A387410, A387411, A387415, A387418.
%K A387419 nonn,new
%O A387419 1,2
%A A387419 _Antti Karttunen_, Sep 01 2025