A322551 Primes indexed by squarefree semiprimes.

13, 29, 43, 47, 73, 79, 101, 137, 139, 149, 163, 167, 199, 233, 257, 269, 271, 293, 313, 347, 373, 389, 421, 439, 443, 449, 467, 487, 491, 499, 577, 607, 631, 647, 653, 673, 677, 727, 751, 757, 811, 821, 823, 829, 839, 907, 929, 937, 947, 983, 1051, 1061, 1093

Offset: 1

Author

Gus Wiseman, Dec 15 2018

Keywords

• nonn

Comments

A squarefree semiprime is a product of two distinct prime numbers.

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. The multiset multisystem with MM-number n is formed by taking the multiset of prime indices of each part of the multiset of prime indices of n. For example, the prime indices of 78 are {1,2,6}, so the multiset multisystem with MM-number 78 is {{},{1},{1,2}}. This sequence lists all MM-numbers of non-loop edges.

Examples

			The sequence of edges whose MM-numbers belong to the sequence begins: {{1,2}}, {{1,3}}, {{1,4}}, {{2,3}}, {{2,4}}, {{1,5}}, {{1,6}}, {{2,5}}, {{1,7}}, {{3,4}}, {{1,8}}, {{2,6}}, {{1,9}}, {{2,7}}, {{3,5}}, {{2,8}}.
		

Crossrefs

Cf. A001358, A003963, A006881, A056239, A085156, A106349, A112798, A302242, A302491, A320458, A320459, A320461.

Programs

Mathematica

Select[Range[100],PrimeOmega[#]==1&&PrimeOmega[PrimePi[#]]==2&&SquareFreeQ[PrimePi[#]]&]

PARI

isok(p) = isprime(p) && (ip=primepi(p)) && (omega(ip)==2) && (bigomega(ip) == 2); \\ Michel Marcus, Dec 16 2018