cp's OEIS Frontend

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

%I A361909 #7 Apr 07 2023 08:57:47
%S A361909 3,14,21,35,49,52,78,117,130,152,182,195,228,273,286,325,338,342,380,
%T A361909 429,455,464,507,513,532,570,637,696,715,798,836,845,855,950,988,1001,
%U A361909 1044,1160,1183,1184,1197,1254,1292,1330,1425,1444,1482,1566,1573,1624
%N A361909 Positive integers > 1 whose prime indices satisfy: (maximum) = 2*(length).
%C A361909 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 A361909 The terms together with their prime indices begin:
%e A361909      3: {2}
%e A361909     14: {1,4}
%e A361909     21: {2,4}
%e A361909     35: {3,4}
%e A361909     49: {4,4}
%e A361909     52: {1,1,6}
%e A361909     78: {1,2,6}
%e A361909    117: {2,2,6}
%e A361909    130: {1,3,6}
%e A361909    152: {1,1,1,8}
%e A361909    182: {1,4,6}
%e A361909    195: {2,3,6}
%e A361909    228: {1,1,2,8}
%e A361909    273: {2,4,6}
%e A361909    286: {1,5,6}
%e A361909    325: {3,3,6}
%e A361909    338: {1,6,6}
%e A361909    342: {1,2,2,8}
%t A361909 Select[Range[2,100],PrimePi[FactorInteger[#][[-1,1]]]==2*PrimeOmega[#]&]
%Y A361909 The LHS is A061395 (greatest prime index), least A055396.
%Y A361909 Without multiplying by 2 in the RHS, we have A106529.
%Y A361909 For omega instead of bigomega we have A111907, counted by A239959.
%Y A361909 Partitions of this type are counted by A237753.
%Y A361909 The RHS is A255201 (twice bigomega).
%Y A361909 For mean instead of length we have A361855, counted by A361853.
%Y A361909 For median instead of length we have A361856, counted by A361849.
%Y A361909 For minimum instead of length we have A361908, counted by A118096.
%Y A361909 A001221 (omega) counts distinct prime factors.
%Y A361909 A001222 (bigomega) counts prime factors with multiplicity.
%Y A361909 A112798 lists prime indices, sum A056239.
%Y A361909 A316413 ranks partitions with integer mean, counted by A067538.
%Y A361909 A326567/A326568 gives mean of prime indices.
%Y A361909 Cf. A067801, A324521, A237752, A237820, A360005, A361205, A361907.
%K A361909 nonn
%O A361909 1,1
%A A361909 _Gus Wiseman_, Apr 05 2023