A361908 - OEIS

%I #6 Apr 07 2023 09:24:14

%S 6,12,18,21,24,36,48,54,63,65,72,96,105,108,133,144,147,162,189,192,

%T 216,288,315,319,324,325,384,432,441,455,481,486,525,567,576,648,715,

%U 731,735,768,845,864,931,945,972,1007,1029,1152,1296,1323,1403,1458,1463

%N Positive integers > 1 whose prime indices satisfy (maximum) = 2*(minimum).

%C 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.

%e The terms together with their prime indices begin:

%e      6: {1,2}

%e     12: {1,1,2}

%e     18: {1,2,2}

%e     21: {2,4}

%e     24: {1,1,1,2}

%e     36: {1,1,2,2}

%e     48: {1,1,1,1,2}

%e     54: {1,2,2,2}

%e     63: {2,2,4}

%e     65: {3,6}

%e     72: {1,1,1,2,2}

%e     96: {1,1,1,1,1,2}

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

%Y The RHS is 2*A055396 (twice minimum).

%Y The LHS is A061395 (greatest prime index).

%Y Partitions of this type are counted by A118096.

%Y For mean instead of minimum we have A361855, counted by A361853.

%Y For median instead of minimum we have A361856, counted by A361849.

%Y For length instead of minimum we have A361909, counted by A237753.

%Y A001221 (omega) counts distinct prime factors.

%Y A001222 (bigomega) counts prime factors with multiplicity.

%Y A112798 lists prime indices, sum A056239.

%Y Cf. A053263, A067801, A237820, A237821, A361858.

%K nonn

%O 1,1

%A _Gus Wiseman_, Apr 05 2023