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

1,1

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.

Links

Table of n, a(n) for n=1..60.

Formula

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

Example

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}

Mathematica

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

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.

Sequence in context: A178724 A087814 A227449 * A113801 A108257 A217252

Adjacent sequences: A371284 A371285 A371286 * A371288 A371289 A371290

Keyword

nonn

Author

Gus Wiseman, Mar 21 2024

Status

approved