A348514 Numbers k for which A003961(k) = 2k+1, where A003961 shifts the prime factorization of n one step towards larger primes.

4, 10, 57, 1054, 2626, 68727, 12371554, 1673018314, 10475647197, 11154517557, 27594844918, 630178495917, 7239182861878

Offset: 1

Author

Antti Karttunen, Oct 29 2021

Keywords

• nonn
• hard
• more

Comments

Numbers k such that A064216(1+k) = k.

It seems that after 4, all other terms are squarefree. See conjecture in A348511.

a(9)..a(13) <= 10475647197, 11154517557, 27594844918, 630178495917, 7239182861878, which are also terms. - David A. Corneth, Oct 30 2021

Links

• Index entries for sequences computed from indices in prime factorization

Crossrefs

Fixed points of map A108228. (Compare to A048674).

Positions of ones in A252748.

Subsequence of the following sequences: A246282, A319630, A348511, A378980 (see also A379216).

Cf. A000230, A003961, A064216, A326134.

Programs

Mathematica

f[p_, e_] := NextPrime[p]^e; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[10^5], s[#] == 2*# + 1 &] (* Amiram Eldar, Oct 30 2021 *)

Extensions

a(9)-a(11) verified by Amiram Eldar, Nov 01 2021

a(12)-a(13) verified by Martin Ehrenstein, Nov 08 2021