cp's OEIS Frontend

A364962 Odd numbers k such that A005941(k) is either k itself or its descendant in Doudna-tree, A005940.

%I A364962 #16 Sep 03 2023 08:43:30
%S A364962 1,3,5,11,19,23,31,37,41,43,47,53,59,61,71,73,79,83,85,89,97,101,103,
%T A364962 107,109,113,127
%N A364962 Odd numbers k such that A005941(k) is either k itself or its descendant in Doudna-tree, A005940.
%C A364962 Questions: Is 85 the only composite in this sequence? (See also A364565). Are there any more terms after 127, or is the sequence finite?
%e A364962 85 = 5*17 is a term, because A005941(85) = 133 = 7*19 = A003961(85), thus 133 is a left hand side child of 85 in the tree depicted in A005940, and therefore 85 is included in this sequence. (See also the last example in A364959).
%o A364962 (PARI)
%o A364962 A005941(n) = { my(f=factor(n), p, p2=1, res=0); for(i=1, #f~, p = 1 << (primepi(f[i, 1])-1); res += (p * p2 * (2^(f[i, 2])-1)); p2 <<= f[i, 2]); (1+res) }; \\ (After _David A. Corneth_'s program for A156552)
%o A364962 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A364962 A252463(n) = if(!(n%2),n/2,A064989(n));
%o A364962 isA364962(n) = if(!(n%2),0,my(k=A005941(n)); while(k>n, k = A252463(k)); (k==n));
%Y A364962 Cf. A005940, A005941, A029747, A156552, A252464.
%Y A364962 Cf. also A364959, A364961.
%K A364962 nonn,hard,more
%O A364962 1,2
%A A364962 _Antti Karttunen_, Aug 14 2023