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A212185
Number of exponents >= 2 in canonical prime factorization of n-th highly composite number (A002182(n)).
2
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, 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, 2, 3, 3, 2, 3, 3, 2, 3, 3, 3, 3, 3, 3, 4, 2, 4, 3, 4, 2
OFFSET
1,7
COMMENTS
Length of row n of A212184 equals a(n) if a(n) is positive, 1 otherwise.
REFERENCES
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.
EXAMPLE
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.
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Matthew Vandermast, Jul 16 2012
STATUS
approved