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.

A212185 Number of exponents >= 2 in canonical prime factorization of n-th highly composite number (A002182(n)).

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%I A212185 #11 Jun 30 2019 10:42:26
%S A212185 0,0,1,0,1,1,2,1,1,1,2,1,2,2,1,2,1,2,2,2,2,2,2,3,2,2,3,2,2,2,2,2,3,2,
%T A212185 2,3,2,2,2,2,2,2,3,2,2,3,2,3,3,2,3,3,2,3,3,2,2,3,2,3,3,2,3,3,2,3,3,2,
%U A212185 2,3,3,2,3,3,2,3,3,3,3,3,3,4,2,4,3,4,2
%N A212185 Number of exponents >= 2 in canonical prime factorization of n-th highly composite number (A002182(n)).
%C A212185 Length of row n of A212184 equals a(n) if a(n) is positive, 1 otherwise.
%D A212185 S. Ramanujan, Highly composite numbers, Proc. Lond. Math. Soc. 14 (1915), 347-409; reprinted in Collected Papers, Ed. G. H. Hardy et al., Cambridge 1927; Chelsea, NY, 1962.
%H A212185 Amiram Eldar, <a href="/A212185/b212185.txt">Table of n, a(n) for n = 1..10000</a>
%H A212185 A. Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/achim/highly.txt">List of the first 1200 highly composite numbers</a>
%H A212185 S. Ramanujan, <a href="http://www.imsc.res.in/~rao/ramanujan/CamUnivCpapers/Cpaper15/page1.htm">Highly Composite Numbers</a>
%e A212185 The canonical prime factorization of 720 (2^4*3^2*5) has 2 exponents that equal or exceed 2. Since 720 = A002182(14), a(14) = 2.
%t A212185 s={}; dm=0; Do[d = DivisorSigma[0, n]; If[d > dm, dm = d; e = FactorInteger[n][[;;,2]]; AppendTo[s, Count[e, _?(# > 1 &)]]], {n, 1, 10^6}]; s (* _Amiram Eldar_, Jun 30 2019 *)
%Y A212185 Cf. A002182, A212172, A212182, A212184.
%K A212185 nonn
%O A212185 1,7
%A A212185 _Matthew Vandermast_, Jul 16 2012