cp's OEIS Frontend

A330103 Numbers whose prime-indices do not have weakly increasing numbers of prime factors, counted with multiplicity.

%I A330103 #9 Feb 07 2021 19:42:50
%S A330103 77,119,154,217,221,231,238,287,308,357,385,403,413,434,437,442,462,
%T A330103 469,476,533,539,551,574,581,589,595,616,651,663,693,713,714,763,767,
%U A330103 770,779,806,817,826,833,847,861,868,871,874,884,889,893,899,924,938
%N A330103 Numbers whose prime-indices do not have weakly increasing numbers of prime factors, counted with multiplicity.
%C A330103 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.
%H A330103 Amiram Eldar, <a href="/A330103/b330103.txt">Table of n, a(n) for n = 1..10000</a>
%e A330103 The sequence of terms together with their corresponding multisets of multisets begins:
%e A330103    77: {{1,1},{3}}
%e A330103   119: {{1,1},{4}}
%e A330103   154: {{},{1,1},{3}}
%e A330103   217: {{1,1},{5}}
%e A330103   221: {{1,2},{4}}
%e A330103   231: {{1},{1,1},{3}}
%e A330103   238: {{},{1,1},{4}}
%e A330103   287: {{1,1},{6}}
%e A330103   308: {{},{},{1,1},{3}}
%e A330103   357: {{1},{1,1},{4}}
%e A330103   385: {{2},{1,1},{3}}
%e A330103 For example, 385 has prime indices {3,4,5} with numbers of prime factors (1,2,1), which is not weakly increasing, so 385 is in the sequence.
%t A330103 Select[Range[1000],!OrderedQ[PrimeOmega/@PrimePi/@First/@FactorInteger[#]]&]
%Y A330103 The version where prime factors are counted without multiplicity is A330281.
%Y A330103 Cf. A001221, A001222, A056239, A112798, A302242, A330098, A330230, A330233.
%K A330103 nonn
%O A330103 1,1
%A A330103 _Gus Wiseman_, Dec 09 2019
%E A330103 Term 667 deleted by _Gus Wiseman_, Feb 07 2021