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%I #45 Dec 20 2024 19:12:57
%S 4,10,57,1054,2626,68727,12371554,1673018314,10475647197,11154517557,
%T 27594844918,630178495917,7239182861878
%N Numbers k for which A003961(k) = 2k+1, where A003961 shifts the prime factorization of n one step towards larger primes.
%C Numbers k such that A064216(1+k) = k.
%C It seems that after 4, all other terms are squarefree. See conjecture in A348511.
%C a(9)..a(13) <= 10475647197, 11154517557, 27594844918, 630178495917, 7239182861878, which are also terms. - _David A. Corneth_, Oct 30 2021
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%t 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 *)
%Y Fixed points of map A108228. (Compare to A048674).
%Y Positions of ones in A252748.
%Y Subsequence of the following sequences: A246282, A319630, A348511, A378980 (see also A379216).
%Y Cf. A000230, A003961, A064216, A326134.
%K nonn,hard,more
%O 1,1
%A _Antti Karttunen_, Oct 29 2021
%E a(9)-a(11) verified by _Amiram Eldar_, Nov 01 2021
%E a(12)-a(13) verified by _Martin Ehrenstein_, Nov 08 2021