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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)). 93
 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 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 A290110 Adjacent sequences:  A181816 A181817 A181818 * A181820 A181821 A181822 KEYWORD nonn,easy,mult,changed AUTHOR Matthew Vandermast, Dec 07 2010 STATUS approved

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Last modified January 15 20:47 EST 2019. Contains 319184 sequences. (Running on oeis4.)