A361909 Positive integers > 1 whose prime indices satisfy: (maximum) = 2*(length).

3, 14, 21, 35, 49, 52, 78, 117, 130, 152, 182, 195, 228, 273, 286, 325, 338, 342, 380, 429, 455, 464, 507, 513, 532, 570, 637, 696, 715, 798, 836, 845, 855, 950, 988, 1001, 1044, 1160, 1183, 1184, 1197, 1254, 1292, 1330, 1425, 1444, 1482, 1566, 1573, 1624

Offset: 1

Author

Gus Wiseman, Apr 05 2023

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}
    14: {1,4}
    21: {2,4}
    35: {3,4}
    49: {4,4}
    52: {1,1,6}
    78: {1,2,6}
   117: {2,2,6}
   130: {1,3,6}
   152: {1,1,1,8}
   182: {1,4,6}
   195: {2,3,6}
   228: {1,1,2,8}
   273: {2,4,6}
   286: {1,5,6}
   325: {3,3,6}
   338: {1,6,6}
   342: {1,2,2,8}
		

Crossrefs

The LHS is A061395 (greatest prime index), least A055396.

Without multiplying by 2 in the RHS, we have A106529.

For omega instead of bigomega we have A111907, counted by A239959.

Partitions of this type are counted by A237753.

The RHS is A255201 (twice bigomega).

For mean instead of length we have A361855, counted by A361853.

For median instead of length we have A361856, counted by A361849.

For minimum instead of length we have A361908, counted by A118096.

A001221 (omega) counts distinct prime factors.

A001222 (bigomega) counts prime factors with multiplicity.

A112798 lists prime indices, sum A056239.

A316413 ranks partitions with integer mean, counted by A067538.

A326567/A326568 gives mean of prime indices.

Cf. A067801, A324521, A237752, A237820, A360005, A361205, A361907.

Programs

Mathematica

Select[Range[2,100],PrimePi[FactorInteger[#][[-1,1]]]==2*PrimeOmega[#]&]