A330103 - OEIS

%I #9 Feb 07 2021 19:42:50

%S 77,119,154,217,221,231,238,287,308,357,385,403,413,434,437,442,462,

%T 469,476,533,539,551,574,581,589,595,616,651,663,693,713,714,763,767,

%U 770,779,806,817,826,833,847,861,868,871,874,884,889,893,899,924,938

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

%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.

%H Amiram Eldar, <a href="/A330103/b330103.txt">Table of n, a(n) for n = 1..10000</a>

%e The sequence of terms together with their corresponding multisets of multisets begins:

%e    77: {{1,1},{3}}

%e   119: {{1,1},{4}}

%e   154: {{},{1,1},{3}}

%e   217: {{1,1},{5}}

%e   221: {{1,2},{4}}

%e   231: {{1},{1,1},{3}}

%e   238: {{},{1,1},{4}}

%e   287: {{1,1},{6}}

%e   308: {{},{},{1,1},{3}}

%e   357: {{1},{1,1},{4}}

%e   385: {{2},{1,1},{3}}

%e 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 Select[Range[1000],!OrderedQ[PrimeOmega/@PrimePi/@First/@FactorInteger[#]]&]

%Y The version where prime factors are counted without multiplicity is A330281.

%Y Cf. A001221, A001222, A056239, A112798, A302242, A330098, A330230, A330233.

%K nonn

%O 1,1

%A _Gus Wiseman_, Dec 09 2019

%E Term 667 deleted by _Gus Wiseman_, Feb 07 2021