%I #20 Mar 09 2017 09:57:50
%S 1,2,3,4,5,6,7,9,11,13,15,17,19,21,23,25,29,31,35,37,41,43,47,49,50,
%T 52,53,55,59,61,65,66,67,71,73,77,79,83,85,89,91,95,97,101,103,107,
%U 109,113,115,119,121,127,131,133,137,139,143,149,151,157,161,163,167,169,173,179,181,186,187,191,193,197,199,203
%N Numbers n such that A003961(n) = A250469(n).
%C Positions of zeros in A280692. Conjectured to be also the positions of ones in A280703.
%C For most terms k of this sequence A003961(k) is also included as a term. Exceptions are: 50, 52, 66, 186, 435, 1245, 1445, 2068, 2085, 11605, ... that seems to be a subsequence of all those terms that have more than two prime factors: 50, 52, 66, 186, 435, 1245, 1445, 2068, 2085, 8695, 11605, ...
%C Note how 8695 = 5*37*47 and A003961(8695) = 7*41*53 = 15211 = A003961(8695) = A250469(8695) (for no apparent reason?).
%H Antti Karttunen, <a href="/A280693/b280693.txt">Table of n, a(n) for n = 1..2001</a>
%t f[n_] := f[n] = Which[n == 1, 1, PrimeQ@ n, NextPrime@ n, True, Times @@ Replace[FactorInteger[n], {p_, e_} :> f[p]^e, 1]]; g[n_] := If[n == 1, 0, PrimePi@ FactorInteger[n][[1, 1]]]; With[{nn = 204}, Function[s, Function[t, Select[Range@ nn, f@ # == t[[#]] &]]@ MapIndexed[Lookup[s, g[First@ #2] + 1][[#1]] - Boole[First@ #2 == 1] &, #] &@ Map[Position[Lookup[s, g@ #], #][[1, 1]] &, Range@ nn]]@ PositionIndex@ Array[g, 10^4]] (* _Michael De Vlieger_, Mar 08 2017, Version 10 *)
%o (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o (define A280693 (ZERO-POS 1 1 A280692))
%Y Fixed points of permutations A266645 & A266646.
%Y Cf. A001222, A003961, A250469, A280692, A280703.
%Y Cf. A000040, A001248, A006094, A251728 (subsequences).
%Y Cf. also arrays A083221 and A246278.
%K nonn
%O 1,2
%A _Antti Karttunen_, Mar 08 2017
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