cp's OEIS Frontend

A387410 Numbers k such that the odd part of (1+k) divides (1 + odd part of A048250(k)), where A048250 is sum of the squarefree divisors of n.

%I A387410 #6 Sep 01 2025 11:23:55
%S A387410 1,3,7,15,31,63,127,255,511,639,1023,2047,2431,4095,5247,8191,14335,
%T A387410 16383,32767,40959,44031,57855,65535,90111,126975,131071,204799,
%U A387410 229375,262143,376831,524287,923647,1048575,1632255,2056191,2097151,2621439,2744319,4194303,6815743,8388607,8781823,16777215,19922943,24068095
%N A387410 Numbers k such that the odd part of (1+k) divides (1 + odd part of A048250(k)), where A048250 is sum of the squarefree divisors of n.
%C A387410 Like in many sequences of this type, the criterion seems to strongly select for numbers with a long tail of trailing 1-bits. The initial 1 is probably the only term that is not in A004767.
%o A387410 (PARI)
%o A387410 A000265(n) = (n>>valuation(n,2));
%o A387410 A048250(n) = factorback(apply(p -> p+1,factor(n)[,1]));
%o A387410 isA387410(n) = !((1+A000265(A048250(n)))%A000265(1+n));
%Y A387410 Cf. A000225 (subsequence), A000265, A004767, A048250.
%Y A387410 For similar sequences, see A336700, A387411, A387415, A387418, A387419.
%K A387410 nonn,new
%O A387410 1,2
%A A387410 _Antti Karttunen_, Sep 01 2025