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A379123 a(n) = A379113(A379121(n)), where A379121 gives those odd squares k for which A379113(k) > 1.

%I A379123 #18 Dec 20 2024 12:35:20
%S A379123 9,121,9,9,81,1521,9,9,49,49,81,9,9,625,49,49,9,961,9,9,9,961,961,49,
%T A379123 9,961,961,169,961,961,16129,49,49,961,961,961,961,961,49,9,9,9,9,625,
%U A379123 961,16129,16129,961,961,961,49,9,49,16129,961,49,961,9,49,49,49,49,9,9,9,9,49,9,16129,9,9,49,49,9,49,9
%N A379123 a(n) = A379113(A379121(n)), where A379121 gives those odd squares k for which A379113(k) > 1.
%C A379123 All terms are odd squares (A016754) by definition.
%C A379123 Among the initial 2025 terms, only the following 12 terms occur:
%C A379123       Term    Occurs     Where
%C A379123               n times
%C A379123 ---------------------------------------------------------------
%C A379123          9      699
%C A379123         49      665
%C A379123         81        2      a(5) and a(11)
%C A379123        121        1      a(2)
%C A379123        169        2      a(28) and a(926)
%C A379123        625        9      at n=14, 44, 85, 110, 155, 447, 654, 896, 1217.
%C A379123        961      390
%C A379123       1521        1      a(6)     NB: 1521 = 9*169.
%C A379123       8649        1      a(1087). NB: 8649 = 9*961.
%C A379123      16129      246
%C A379123   67092481        8      First occurrence at a(1120)
%C A379123 3287531569        1      a(1636). NB: 3287531569 = 49*67092481.
%C A379123 Questions: Is this sequence infinite? Do all terms of A133049 eventually appear here? Or any 4th or higher powers of Mersenne and other primes, apart from 81 and 625?
%H A379123 Antti Karttunen, <a href="/A379123/b379123.txt">Table of n, a(n) for n = 1..2025</a>
%H A379123 <a href="/index/Con#CongruCrossDomain">Index entries for sequences defined by congruent products between domains N and GF(2)[X]</a>.
%H A379123 <a href="/index/Ge#GF2X">Index entries for sequences related to polynomials in ring GF(2)[X]</a>.
%H A379123 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.
%F A379123 a(n) = A379121(n) / A379124(n).
%e A379123 See examples in A379121.
%o A379123 (PARI) forstep(n=1,2^18,2,d=A379113(n^2); if(d>1, print1(d,", ")));
%Y A379123 Cf. A016754, A114390, A133049, A379113, A379121, A379124, A379125.
%K A379123 nonn
%O A379123 1,1
%A A379123 _Antti Karttunen_, Dec 18 2024