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%I #7 Dec 11 2024 17:57:25
%S 2,5,7,17,20,28,35,41,43,45,49,52,57,64,69,81,83,98,109,120,140,144,
%T 152,171,173,176,178,182,190,206,215,225,230,236,253,256,262,277,286,
%U 294,296,302,307,315,318,323,336,346,373,377,390,395,405,428,430,444
%N Lesser prime index of twin primes with nonsquarefree mean.
%C A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%C This is a subset of A029707 (twin prime indices). The other twin primes are A068361, so A029707 is the disjoint union of A068361 and A378620.
%F prime(a(n)) = A061368(n).
%t Select[Range[100],Prime[#]+2==Prime[#+1]&&!SquareFreeQ[Prime[#]+1]&]
%Y The lesser of twin primes is A001359, index A029707 (complement A049579).
%Y The greater of twin primes is A006512, index A107770 (complement appears to be A168543).
%Y A subset of A029707 (twin prime lesser indices).
%Y Prime indices of the primes listed by A061368.
%Y Indices of twin primes with squarefree mean are A068361.
%Y A000040 lists the primes, differences A001223, (run-lengths A333254, A373821).
%Y A005117 lists the squarefree numbers, differences A076259.
%Y A006562 finds balanced primes.
%Y A013929 lists the nonsquarefree numbers, differences A078147.
%Y A014574 is the intersection of A006093 and A008864.
%Y A038664 finds the first position of a prime gap of 2n.
%Y A046933 counts composite numbers between primes.
%Y A120327 gives the least nonsquarefree number >= n.
%Y Cf. A007674, A072284, A068360.
%Y Cf. A057627, A061398, A061399, A067535, A070321, A071403, A112925.
%Y Cf. A000720, A025584, A067774, A122535, A155752, A179067.
%K nonn,new
%O 1,1
%A _Gus Wiseman_, Dec 10 2024