cp's OEIS Frontend

A387415 Numbers k such that the odd part of (1+k) divides (1 + odd part of A001615(k)), where A001615 is Dedekind's psi-function.

%I A387415 #5 Sep 01 2025 11:24:00
%S A387415 1,3,7,15,31,63,127,255,511,1023,2047,2431,4095,8191,14335,16383,
%T A387415 27135,32767,44031,57855,65535,75775,131071,204799,262143,376831,
%U A387415 524287,667135,923647,1048575,1441791,1632255,2056191,2097151,2315775,2744319,4194303,6768639,6815743,8388607,8781823,16777215,19922943,24068095
%N A387415 Numbers k such that the odd part of (1+k) divides (1 + odd part of A001615(k)), where A001615 is Dedekind's psi-function.
%C A387415 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 A387415 (PARI)
%o A387415 A000265(n) = (n>>valuation(n,2));
%o A387415 A001615(n) = if(1==n,n, my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1)));
%o A387415 isA387415(n) = !((1+A000265(A001615(n)))%A000265(1+n));
%Y A387415 Cf. A000225 (subsequence), A000265, A001615.
%Y A387415 For similar sequences, see A336700, A387410, A387418, A387419.
%K A387415 nonn,new
%O A387415 1,2
%A A387415 _Antti Karttunen_, Sep 01 2025