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A181819 a(1) = 1; for n>1, if n = Product prime(i)^e(i), then a(n) = Product prime(e(i)). 178
1, 2, 2, 3, 2, 4, 2, 5, 3, 4, 2, 6, 2, 4, 4, 7, 2, 6, 2, 6, 4, 4, 2, 10, 3, 4, 5, 6, 2, 8, 2, 11, 4, 4, 4, 9, 2, 4, 4, 10, 2, 8, 2, 6, 6, 4, 2, 14, 3, 6, 4, 6, 2, 10, 4, 10, 4, 4, 2, 12, 2, 4, 6, 13, 4, 8, 2, 6, 4, 8, 2, 15, 2, 4, 6, 6, 4, 8, 2, 14, 7, 4, 2, 12, 4, 4, 4, 10, 2, 12, 4, 6, 4, 4, 4, 22, 2, 6, 6, 9, 2, 8, 2, 10, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) depends only on prime signature of n (cf. A025487). a(m) = a(n) iff m and n have the same prime signature.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for sequences computed from exponents in factorization of n

FORMULA

From Antti Karttunen, Feb 05 & 07 2016: (Start)

a(1) = 1; for n > 1, a(n) = A000040(A067029(n)) * a(A028234(n)).

a(1) = 1; for n > 1, a(n) = A008578(A001511(n)) * a(A064989(n)).

Other identities. For all n >= 1:

a(A124859(n)) = A122111(a(n)) = A238745(n). - from Matthew Vandermast's formulas for the latter sequence.

(End)

a(n) = A246029(A156552(n)). - Antti Karttunen, Oct 15 2016

EXAMPLE

20 = 2^2*5 has the exponents (2,1) in its prime factorization. Accordingly, a(20) = prime(2)*prime(1) (i.e., A000040(1)*A000040(1)), which equals 3*2 = 6.

MAPLE

A181819 := proc(n)

    local a;

    a := 1;

    for pf in ifactors(n)[2] do

        a := a*ithprime(pf[2]) ;

    end do:

    a ;

end proc:

seq(A181819(n), n=1..80) ; # R. J. Mathar, Jan 09 2019

MATHEMATICA

{1}~Join~Table[Times @@ Prime@ Map[Last, FactorInteger@ n], {n, 2, 120}] (* Michael De Vlieger, Feb 07 2016 *)

PROG

(Haskell)

a181819 = product . map a000040 . a124010_row

-- Reinhard Zumkeller, Mar 26 2012

(PARI) a(n) = {my(f=factor(n)); prod(k=1, #f~, prime(f[k, 2])); } \\ Michel Marcus, Nov 16 2015

(Scheme, with memoization-macro definec, two variants)

(definec (A181819 n) (cond ((= 1 n) 1) (else (* (A000040 (A067029 n)) (A181819 (A028234 n))))))

(definec (A181819 n) (cond ((= 1 n) 1) ((even? n) (* (A000040 (A007814 n)) (A181819 (A000265 n)))) (else (A181819 (A064989 n)))))

;; Antti Karttunen, Feb 05 & 07 2016

CROSSREFS

Cf. A000040, A000265, A001511, A007814, A008578, A028234, A064989, A067029, A122111, A124010, A124859, A156552, A181820, A181821, A182850, A115621, A101296, A238690, A238745, A238748, A246029.

Sequence in context: A305899 A101296 A305898 * A302046 A077462 A324203

Adjacent sequences:  A181816 A181817 A181818 * A181820 A181821 A181822

KEYWORD

nonn,easy,mult

AUTHOR

Matthew Vandermast, Dec 07 2010

STATUS

approved

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Last modified September 20 16:48 EDT 2019. Contains 327242 sequences. (Running on oeis4.)