|
%I #5 Mar 22 2024 08:59:51
%S 13,15,26,29,30,33,35,37,39,43,45,47,51,52,55,58,60,61,65,66,69,70,71,
%T 73,74,75,77,78,79,85,86,87,89,90,91,93,94,95,99,101,102,104,105,107,
%U 110,111,116,117,119,120,122,123,129,130,132,135,137,138,139,140
%N Numbers whose product of prime indices has exactly two distinct prime factors.
%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.
%F A001221(A003963(a(n))) = A303975(a(n)) = 2.
%e The terms together with their prime indices begin:
%e 13: {6}
%e 15: {2,3}
%e 26: {1,6}
%e 29: {10}
%e 30: {1,2,3}
%e 33: {2,5}
%e 35: {3,4}
%e 37: {12}
%e 39: {2,6}
%e 43: {14}
%e 45: {2,2,3}
%e 47: {15}
%e 51: {2,7}
%e 52: {1,1,6}
%e 55: {3,5}
%e 58: {1,10}
%e 60: {1,1,2,3}
%t Select[Range[100],2==PrimeNu[Times @@ PrimePi/@First/@If[#==1,{},FactorInteger[#]]]&]
%Y Positions of 2's in A303975 (positions of 1's are A320698).
%Y Counting divisors (not factors) gives A371127, positions of 2's in A370820.
%Y A000005 counts divisors.
%Y A000961 lists powers of primes, of prime index A302596.
%Y A001221 counts distinct prime factors.
%Y A001358 lists semiprimes, squarefree A006881.
%Y A003963 gives product of prime indices.
%Y A027746 lists prime factors, indices A112798, length A001222.
%Y A076610 lists products of primes of prime index.
%Y A355731 counts choices of a divisor of each prime index, firsts A355732.
%Y A355741 counts choices of a prime factor of each prime index.
%Y Cf. A000079, A007416, A056239, A302540, A319899, A336101, A355739, A370802.
%K nonn
%O 1,1
%A _Gus Wiseman_, Mar 21 2024
|
