cp's OEIS Frontend

A320324 Numbers of which each prime index has the same number of prime factors, counted with multiplicity.

%I A320324 #21 Feb 07 2021 06:26:01
%S A320324 1,2,3,4,5,7,8,9,11,13,15,16,17,19,23,25,27,29,31,32,33,37,41,43,45,
%T A320324 47,49,51,53,55,59,61,64,67,71,73,75,79,81,83,85,89,91,93,97,99,101,
%U A320324 103,107,109,113,121,123,125,127,128,131,135,137,139,149,151,153
%N A320324 Numbers of which each prime index has the same number of prime factors, counted with multiplicity.
%C A320324 A prime index of n is a number m such that prime(m) divides n.
%H A320324 Amiram Eldar, <a href="/A320324/b320324.txt">Table of n, a(n) for n = 1..10000</a>
%H A320324 Gus Wiseman, <a href="/A038041/a038041.txt">Sequences counting and ranking multiset partitions whose part lengths, sums, or averages are constant or strict.</a>
%e A320324 The terms together with their corresponding multiset multisystems (A302242):
%e A320324    1: {}
%e A320324    2: {{}}
%e A320324    3: {{1}}
%e A320324    4: {{},{}}
%e A320324    5: {{2}}
%e A320324    7: {{1,1}}
%e A320324    8: {{},{},{}}
%e A320324    9: {{1},{1}}
%e A320324   11: {{3}}
%e A320324   13: {{1,2}}
%e A320324   15: {{1},{2}}
%e A320324   16: {{},{},{},{}}
%e A320324   17: {{4}}
%e A320324   19: {{1,1,1}}
%e A320324   23: {{2,2}}
%e A320324   25: {{2},{2}}
%e A320324   27: {{1},{1},{1}}
%e A320324   29: {{1,3}}
%e A320324   31: {{5}}
%e A320324   32: {{},{},{},{},{}}
%e A320324   33: {{1},{3}}
%e A320324   37: {{1,1,2}}
%e A320324   41: {{6}}
%e A320324   43: {{1,4}}
%e A320324   45: {{1},{1},{2}}
%e A320324   47: {{2,3}}
%e A320324   49: {{1,1},{1,1}}
%t A320324 Select[Range[100],SameQ@@PrimeOmega/@PrimePi/@First/@FactorInteger[#]&]
%o A320324 (PARI) is(n) = #Set(apply(p -> bigomega(primepi(p)), factor(n)[,1]~))<=1 \\ _Rémy Sigrist_, Oct 11 2018
%Y A320324 Cf. A001222, A038041, A112798, A302242, A306017, A317583, A319066, A319169, A320325, A322794, A326533, A326534, A326535, A326536, A326537.
%K A320324 nonn
%O A320324 1,2
%A A320324 _Gus Wiseman_, Oct 10 2018