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A348514
Numbers k for which A003961(k) = 2k+1, where A003961 shifts the prime factorization of n one step towards larger primes.
3
4, 10, 57, 1054, 2626, 68727, 12371554, 1673018314, 10475647197, 11154517557, 27594844918, 630178495917, 7239182861878
OFFSET
1,1
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
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 *)
CROSSREFS
Fixed points of map A108228. (Compare to A048674).
Positions of ones in A252748.
Subsequence of A246282, of A319630, and of A348511.
Sequence in context: A002290 A336997 A222569 * A254078 A104363 A092190
KEYWORD
nonn,hard,more
AUTHOR
Antti Karttunen, Oct 29 2021
EXTENSIONS
a(9)-a(11) verified by Amiram Eldar, Nov 01 2021
a(12)-a(13) verified by Martin Ehrenstein, Nov 08 2021
STATUS
approved