A338555 Numbers that are either a power of a prime or have relatively prime prime indices.

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, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 64, 66, 67, 68, 69, 70, 71, 72

Offset: 1

Author

Gus Wiseman, Nov 03 2020

Keywords

• nonn

Comments

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.

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.

Crossrefs

A327534 uses primes instead of prime powers.

A338331 is the pairwise coprime version, with complement A338330.

A338552 is the complement.

A338553 counts the partitions with these Heinz numbers.

A000837 counts relatively prime partitions, with Heinz numbers A289509.

A000961 lists powers of primes.

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

A051424 counts pairwise coprime or singleton partitions.

A291166 ranks relatively prime compositions, with complement A291165.

A327516 counts pairwise coprime partitions, with Heinz numbers A302696.

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

Programs

Mathematica

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

Formula

Equals A000961 \/ A289509.

Complement of A024619 /\ A318978.