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.

A075592 Numbers n such that number of distinct prime divisors of n is a divisor of n.

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%I A075592 #29 Jul 10 2020 03:49:53
%S A075592 2,3,4,5,6,7,8,9,10,11,12,13,14,16,17,18,19,20,22,23,24,25,26,27,28,
%T A075592 29,30,31,32,34,36,37,38,40,41,42,43,44,46,47,48,49,50,52,53,54,56,58,
%U A075592 59,60,61,62,64,66,67,68,71,72,73,74,76,78,79,80,81,82,83,84,86,88,89,90
%N A075592 Numbers n such that number of distinct prime divisors of n is a divisor of n.
%C A075592 Numbers n such that omega(n) divides n.
%C A075592 The asymptotic density of this sequence is 0 (Cooper and Kennedy, 1989). - _Amiram Eldar_, Jul 10 2020
%H A075592 Christian N. K. Anderson, <a href="/A075592/b075592.txt">Table of n, a(n) for n = 1..10000</a>
%H A075592 Curtis N. Cooper, Robert E. Kennedy, <a href="http://www.jstor.org/stable/2323194">Chebyshev's inequality and natural density</a>, Amer. Math. Monthly 96 (1989), no. 2, 118-124.
%t A075592 Select[Range[2,100],Divisible[#,Length[Select[Divisors[#], PrimeQ]]]&]  (* _Harvey P. Dale_, Mar 17 2011 *)
%o A075592 (R) library(gmp); omega<-function(x) length(unique(as.numeric(factorize(x))))
%o A075592 which(c(F,vapply(2:100,function(n) isint(n/omega(n)),T))) # _Christian N. K. Anderson_, Apr 25 2013
%o A075592 (PARI) isok(n) = iferr(!(n % omega(n)), E, 0); \\ _Michel Marcus_, Oct 06 2017
%Y A075592 Different from A070776: 78 belongs to this sequence but not to A070776.
%Y A075592 Cf. A185307 (complement), A001221, A001222, A074946 (BigOmega(n) divides n).
%K A075592 easy,nonn
%O A075592 1,1
%A A075592 _Amarnath Murthy_, Sep 26 2002
%E A075592 More terms from _David Wasserman_, Jan 20 2005
%E A075592 "Distinct" added to name by _Christian N. K. Anderson_, Apr 23 2013