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A162642 Number of odd exponents in the canonical prime factorization of n. 4
0, 1, 1, 0, 1, 2, 1, 1, 0, 2, 1, 1, 1, 2, 2, 0, 1, 1, 1, 1, 2, 2, 1, 2, 0, 2, 1, 1, 1, 3, 1, 1, 2, 2, 2, 0, 1, 2, 2, 2, 1, 3, 1, 1, 1, 2, 1, 1, 0, 1, 2, 1, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1, 0, 2, 3, 1, 1, 2, 3, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 0, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 1, 1, 1, 0, 1, 3, 1, 2, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

a(n) is also known as the squarefree rank of n. - Jason Kimberley, Jul 08 2017

REFERENCES

R. B. Eggleton, J. S. Kimberley and J. A. MacDougall, Square-free rank of integers, to appear.

LINKS

Jason Kimberley, Table of n, a(n) for n = 1..20000

FORMULA

a(n) = A001221(n) - A162641(n).

a(n) = A001221(A007913(n)). - Jason Kimberley, Jan 06 2016

a(A000290(n)) = 0, n>0. - Michel Marcus, Jan 08 2016

G.f.: Sum_{i>=1} Sum_{j>=1} (-1)^j x^(prime(i)^j)/(x^(prime(i)^j) - 1). - Robert Israel, Jan 15 2016

MAPLE

A162642 := proc(n) add ( op(2, f) mod 2 , f=ifactors(n)[2]) ; end proc: # R. J. Mathar, Mar 30 2011

MATHEMATICA

{0}~Join~Table[Count[Last /@ FactorInteger@ n, e_ /; OddQ@ e], {n, 2, 105}] (* Michael De Vlieger, Jan 06 2016 *)

PROG

(MAGMA) A162642:=func<n|#{pe:pe in Factorisation(n)|IsOdd(pe[2])}>;

[A162642(n):n in[1..105]]; // Jason Kimberley, Dec 30 2015

(PARI) a(n) = {my(f = factor(n)); sum(k=1, #f~, f[k, 2] % 2); } \\ Michel Marcus, Jan 08 2016

CROSSREFS

Cf. A001221, A002035, A007913, A162641.

Sequence in context: A029369 A255315 A125072 * A139146 A277487 A144032

Adjacent sequences:  A162639 A162640 A162641 * A162643 A162644 A162645

KEYWORD

nonn,easy,changed

AUTHOR

Reinhard Zumkeller, Jul 08 2009

STATUS

approved

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Last modified July 22 03:22 EDT 2017. Contains 289648 sequences.