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

1, 3, 5, 11, 19, 23, 31, 37, 41, 43, 47, 53, 59, 61, 71, 73, 79, 83, 85, 89, 97, 101, 103, 107, 109, 113, 127

Offset

1,2

Comments

Questions: Is 85 the only composite in this sequence? (See also A364565). Are there any more terms after 127, or is the sequence finite?

Links

Table of n, a(n) for n=1..27.

Example

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).

Prog

(PARI)
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)
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)};
A252463(n) = if(!(n%2), n/2, A064989(n));
isA364962(n) = if(!(n%2), 0, my(k=A005941(n)); while(k>n, k = A252463(k)); (k==n));

Crossrefs

Cf. A005940, A005941, A029747, A156552, A252464.

Cf. also A364959, A364961.

Sequence in context: A306895 A198519 A045957 * A153065 A089439 A122516

Adjacent sequences: A364959 A364960 A364961 * A364963 A364964 A364965

Keyword

nonn,hard,more

Author

Antti Karttunen, Aug 14 2023

Status

approved