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A355392 Sorted positions of first appearances in A181591 = binomial(bigomega(n), omega(n)).

%I A355392 #13 Jul 10 2022 13:22:11
%S A355392 1,4,8,16,24,32,48,96,128,192,240,256,384,480,512,768,960,1536,1920,
%T A355392 2048,3072,3360,3840,4096,6144,6720,7680,8192,12288,13440,15360,16384,
%U A355392 24576,26880,30720,49152,53760,61440,65536,73920,107520,122880,131072,147840,196608
%N A355392 Sorted positions of first appearances in A181591 = binomial(bigomega(n), omega(n)).
%C A355392 These are the positions of terms in A181591 that are different from all prior terms.
%C A355392 The statistic omega = A001221 counts distinct prime factors (without multiplicity).
%C A355392 The statistic bigomega = A001222 counts prime factors with multiplicity.
%C A355392 We have A181591(2^k) = k, so the image under A181591 is a permutation of the positive integers. It begins: 1, 2, 3, 4, 6, 5, 10, 15, 7, 21, 20, ...
%H A355392 Amiram Eldar, <a href="/A355392/b355392.txt">Table of n, a(n) for n = 1..210</a>
%e A355392 The terms together with their prime indices begin:
%e A355392     1: {}
%e A355392     4: {1,1}
%e A355392     8: {1,1,1}
%e A355392    16: {1,1,1,1}
%e A355392    24: {1,1,1,2}
%e A355392    32: {1,1,1,1,1}
%e A355392    48: {1,1,1,1,2}
%e A355392    96: {1,1,1,1,1,2}
%e A355392   128: {1,1,1,1,1,1,1}
%e A355392   192: {1,1,1,1,1,1,2}
%e A355392   240: {1,1,1,1,2,3}
%e A355392   256: {1,1,1,1,1,1,1,1}
%e A355392   384: {1,1,1,1,1,1,1,2}
%e A355392   480: {1,1,1,1,1,2,3}
%e A355392   512: {1,1,1,1,1,1,1,1,1}
%e A355392   768: {1,1,1,1,1,1,1,1,2}
%e A355392   960: {1,1,1,1,1,1,2,3}
%t A355392 s=Table[Binomial[PrimeOmega[n],PrimeNu[n]],{n,1000}];
%t A355392 Select[Range[Length[s]],FreeQ[Take[s,#-1],s[[#]]]&]
%Y A355392 The unsorted version with multiplicity is A355386.
%Y A355392 This is the sorted version of A355391.
%Y A355392 A000005 counts divisors.
%Y A355392 A001221 counts prime indices without multiplicity.
%Y A355392 A001222 count prime indices with multiplicity.
%Y A355392 A070175 gives representatives for bigomega and omega, triangle A303555.
%Y A355392 Cf. A000712, A022811, A056239, A071625, A118914, A181819, A323023, A355384.
%K A355392 nonn
%O A355392 1,2
%A A355392 _Gus Wiseman_, Jul 04 2022
%E A355392 a(41)-a(45) from _Amiram Eldar_, Jul 10 2022