A371287 Numbers whose product of prime indices has exactly two distinct prime factors.

13, 15, 26, 29, 30, 33, 35, 37, 39, 43, 45, 47, 51, 52, 55, 58, 60, 61, 65, 66, 69, 70, 71, 73, 74, 75, 77, 78, 79, 85, 86, 87, 89, 90, 91, 93, 94, 95, 99, 101, 102, 104, 105, 107, 110, 111, 116, 117, 119, 120, 122, 123, 129, 130, 132, 135, 137, 138, 139, 140

Offset: 1

Author

Gus Wiseman, Mar 21 2024

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.

Examples

			The terms together with their prime indices begin:
  13: {6}
  15: {2,3}
  26: {1,6}
  29: {10}
  30: {1,2,3}
  33: {2,5}
  35: {3,4}
  37: {12}
  39: {2,6}
  43: {14}
  45: {2,2,3}
  47: {15}
  51: {2,7}
  52: {1,1,6}
  55: {3,5}
  58: {1,10}
  60: {1,1,2,3}
		

Crossrefs

Positions of 2's in A303975 (positions of 1's are A320698).

Counting divisors (not factors) gives A371127, positions of 2's in A370820.

A000005 counts divisors.

A000961 lists powers of primes, of prime index A302596.

A001221 counts distinct prime factors.

A001358 lists semiprimes, squarefree A006881.

A003963 gives product of prime indices.

A027746 lists prime factors, indices A112798, length A001222.

A076610 lists products of primes of prime index.

A355731 counts choices of a divisor of each prime index, firsts A355732.

A355741 counts choices of a prime factor of each prime index.

Cf. A000079, A007416, A056239, A302540, A319899, A336101, A355739, A370802.

Programs

Mathematica

Select[Range[100],2==PrimeNu[Times @@ PrimePi/@First/@If[#==1,{},FactorInteger[#]]]&]

Formula

A001221(A003963(a(n))) = A303975(a(n)) = 2.