A371127 Powers of 2 times powers > 1 of a prime-indexed prime number.

3, 5, 6, 9, 10, 11, 12, 17, 18, 20, 22, 24, 25, 27, 31, 34, 36, 40, 41, 44, 48, 50, 54, 59, 62, 67, 68, 72, 80, 81, 82, 83, 88, 96, 100, 108, 109, 118, 121, 124, 125, 127, 134, 136, 144, 157, 160, 162, 164, 166, 176, 179, 191, 192, 200, 211, 216, 218, 236, 241

Offset: 1

Author

Gus Wiseman, Mar 18 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:
      3: {2}
      5: {3}
      6: {1,2}
      9: {2,2}
     10: {1,3}
     11: {5}
     12: {1,1,2}
     17: {7}
     18: {1,2,2}
     20: {1,1,3}
     22: {1,5}
     24: {1,1,1,2}
     25: {3,3}
     27: {2,2,2}
     31: {11}
     34: {1,7}
     36: {1,1,2,2}
		

Crossrefs

Subset of A302540.

Subset of A336101 = powers of 2 times powers of primes.

Positions of 2's in A370820.

Counting prime factors instead of divisors gives A371287.

A000005 counts divisors.

A000961 lists powers of primes, A302596 of prime index.

A001221 counts distinct prime factors.

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, A005179, A007416, A303975, A319899, A355739, A370348, A370802, A371165-A371170, A371178.

Programs

Mathematica

Select[Range[100],Length[Union @@ Divisors/@PrimePi/@First/@If[#==1,{},FactorInteger[#]]]==2&]