cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A320913 Numbers with an even number of prime factors (counted with multiplicity) that cannot be factored into squarefree semiprimes (A320891) but can be factored into distinct semiprimes (A320912).

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%I A320913 #6 Dec 08 2018 21:03:52
%S A320913 4,9,24,25,40,49,54,56,88,104,121,135,136,152,169,184,189,232,240,248,
%T A320913 250,289,296,297,328,336,344,351,361,375,376,424,459,472,488,513,528,
%U A320913 529,536,560,568,584,621,624,632,664,686,712,776,783,808,810,816,824
%N A320913 Numbers with an even number of prime factors (counted with multiplicity) that cannot be factored into squarefree semiprimes (A320891) but can be factored into distinct semiprimes (A320912).
%C A320913 A semiprime (A001358) is a product of any two not necessarily distinct primes.
%C A320913 If A025487(k) is contained in this sequence then so is every positive integer with its prime signature. - _David A. Corneth_, Oct 24 2018
%t A320913 sqfsemfacs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[sqfsemfacs[n/d],Min@@#>=d&]],{d,Select[Rest[Divisors[n]],And[SquareFreeQ[#],PrimeOmega[#]==2]&]}]];
%t A320913 strsemfacs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[strsemfacs[n/d],Min@@#>d&]],{d,Select[Rest[Divisors[n]],PrimeOmega[#]==2&]}]];
%t A320913 Select[Range[1000],And[EvenQ[PrimeOmega[#]],strsemfacs[#]!={},sqfsemfacs[#]=={}]&]
%Y A320913 Cf. A001055, A001222, A001358, A005117, A006881, A007717, A025487, A028260, A320655, A320656, A320891, A320892, A320893, A320894, A320911, A320912.
%K A320913 nonn
%O A320913 1,1
%A A320913 _Gus Wiseman_, Oct 23 2018