A322551 - OEIS

%I #6 Dec 16 2018 17:58:48

%S 13,29,43,47,73,79,101,137,139,149,163,167,199,233,257,269,271,293,

%T 313,347,373,389,421,439,443,449,467,487,491,499,577,607,631,647,653,

%U 673,677,727,751,757,811,821,823,829,839,907,929,937,947,983,1051,1061,1093

%N Primes indexed by squarefree semiprimes.

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

%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. 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.

%e 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}}.

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

%o (PARI) isok(p) = isprime(p) && (ip=primepi(p)) && (omega(ip)==2) && (bigomega(ip) == 2); \\ _Michel Marcus_, Dec 16 2018

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

%K nonn

%O 1,1

%A _Gus Wiseman_, Dec 15 2018