A327900 Nonprime squarefree numbers whose prime indices all have the same Omega (number of prime factors counted with multiplicity).

1, 15, 33, 51, 55, 85, 91, 93, 123, 155, 161, 165, 177, 187, 201, 203, 205, 249, 255, 295, 299, 301, 327, 329, 335, 341, 377, 381, 415, 451, 465, 471, 511, 527, 537, 545, 553, 559, 561, 573, 611, 615, 633, 635, 649, 667, 679, 697, 703, 707, 723, 737, 785, 831

Offset: 1

Author

Gus Wiseman, Sep 30 2019

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 sequence of terms together with their prime indices begins:
    1: {}
   15: {2,3}
   33: {2,5}
   51: {2,7}
   55: {3,5}
   85: {3,7}
   91: {4,6}
   93: {2,11}
  123: {2,13}
  155: {3,11}
  161: {4,9}
  165: {2,3,5}
  177: {2,17}
  187: {5,7}
  201: {2,19}
  203: {4,10}
  205: {3,13}
  249: {2,23}
  255: {2,3,7}
  295: {3,17}
		

Links

• Gus Wiseman, Sequences counting and ranking multiset partitions whose part lengths, sums, or averages are constant or strict.

Crossrefs

The case including primes and nonsquarefree numbers is A320324.

The version for sum of prime indices is A327901.

The version for mean of prime indices is A327902.

Cf. A001222, A038041, A056239, A078175, A112798, A306017, A306021, A316413, A317583, A322794, A327908.

Programs

Mathematica

Select[Range[1000],!PrimeQ[#]&&SquareFreeQ[#]&&SameQ@@PrimeOmega/@PrimePi/@First/@FactorInteger[#]&]