A338555 - OEIS

%I #10 Nov 20 2020 17:18:55

%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,22,23,24,25,26,27,

%T 28,29,30,31,32,33,34,35,36,37,38,40,41,42,43,44,45,46,47,48,49,50,51,

%U 52,53,54,55,56,58,59,60,61,62,64,66,67,68,69,70,71,72

%N Numbers that are either a power of a prime or have relatively prime prime indices.

%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 Also Heinz numbers of partitions either constant or relatively prime (A338553). The Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), giving a bijective correspondence between positive integers and integer partitions.

%F Equals A000961 \/ A289509.

%F Complement of A024619 /\ A318978.

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

%Y A327534 uses primes instead of prime powers.

%Y A338331 is the pairwise coprime version, with complement A338330.

%Y A338552 is the complement.

%Y A338553 counts the partitions with these Heinz numbers.

%Y A000837 counts relatively prime partitions, with Heinz numbers A289509.

%Y A000961 lists powers of primes.

%Y A018783 counts partitions whose prime indices are not relatively prime, with Heinz numbers A318978.

%Y A051424 counts pairwise coprime or singleton partitions.

%Y A291166 ranks relatively prime compositions, with complement A291165.

%Y A327516 counts pairwise coprime partitions, with Heinz numbers A302696.

%Y Cf. A000740, A056239, A108572, A112798, A302569, A302796, A327685, A328677.

%K nonn

%O 1,2

%A _Gus Wiseman_, Nov 03 2020