A320698 Numbers whose product of prime indices is a prime power (A246655).

3, 5, 6, 7, 9, 10, 11, 12, 14, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 31, 34, 36, 38, 40, 41, 42, 44, 46, 48, 49, 50, 53, 54, 56, 57, 59, 62, 63, 67, 68, 72, 76, 80, 81, 82, 83, 84, 88, 92, 96, 97, 98, 100, 103, 106, 108, 109, 112, 114, 115, 118, 121, 124

Offset: 1

Author

Gus Wiseman, Oct 19 2018

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 numbers whose prime indices are all powers of a common prime number.

Examples

			The sequence of all integer partitions whose Heinz numbers belong to the sequence begins: (2), (3), (1,2), (4), (2,2), (1,3), (5), (1,1,2), (1,4), (7), (1,2,2), (8), (1,1,3), (2,4), (1,5), (9), (1,1,1,2), (3,3), (2,2,2), (1,1,4), (11), (1,7), (1,1,2,2), (1,8), (1,1,1,3), (13), (1,2,4), (1,1,5), (1,9), (1,1,1,1,2), (4,4), (1,3,3), (16), (1,2,2,2), (1,1,1,4), (2,8).
		

Links

• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000720, A000961, A001597, A003963, A047968, A056239, A064573, A112798, A246547, A246655, A279787, A320322, A320325, A320699, A320700.

Programs

Mathematica

Select[Range[100],PrimePowerQ[Times@@Cases[FactorInteger[#],{p_,k_}:>PrimePi[p]^k]]&]

PARI

is(n) = my(f=factor(n)[, 1]~, p=1); for(k=1, #f, p=p*primepi(f[k])); isprimepower(p) \\ Felix Fröhlich, Oct 20 2018