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Numbers that are 1, prime, or whose prime indices are relatively prime.
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%I #5 Sep 18 2019 04:57:49

%S 1,2,3,4,5,6,7,8,10,11,12,13,14,15,16,17,18,19,20,22,23,24,26,28,29,

%T 30,31,32,33,34,35,36,37,38,40,41,42,43,44,45,46,47,48,50,51,52,53,54,

%U 55,56,58,59,60,61,62,64,66,67,68,69,70,71,72,73,74,75,76

%N Numbers that are 1, prime, or whose prime indices are relatively prime.

%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. Numbers whose prime indices are relatively prime are A289509.

%H Gus Wiseman, <a href="https://docs.google.com/document/d/e/2PACX-1vSX9dPMGJhxB8rOknCGvOs6PiyhupdWNpqLsnphdgU6MEVqFBnWugAXidDhwHeKqZe_YnUqYeGOXsOk/pub">Sequences counting and encoding certain classes of multisets</a>

%F Equals the union of {1}, A000040, and A289509.

%e 91 = 7 * 13 has prime indices {4,6}, which have a common divisor of 2, so 91 is not in the sequence.

%t Select[Range[100],#==1||PrimeQ[#]||GCD@@PrimePi/@First/@FactorInteger[#]==1&]

%Y See link for additional cross-references.

%Y Complement of A327407.

%Y Cf. A056239, A112798, A281116, A289509, A302569.

%K nonn

%O 1,2

%A _Gus Wiseman_, Sep 17 2019