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 A053164 4th root of largest 4th power dividing n. 18
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,16 COMMENTS Multiplicative with a(p^e) = p^[e/4]. - Mitch Harris, Apr 19 2005 LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 Henry Bottomley, Some Smarandache-type multiplicative sequences. FORMULA a(n) = A000188(A000188(n)) = A008835(n)^(1/4). Multiplicative with a(p^e) = p^[e/4]. Dirichlet g.f.: zeta(4s-1)*zeta(s)/zeta(4s). - R. J. Mathar, Apr 09 2011 Sum_{k=1..n} a(k) ~ 90*zeta(3)*n/Pi^4 + 3*zeta(1/2)*sqrt(n)/Pi^2. - Vaclav Kotesovec, Dec 01 2020 a(n) = Sum_{d^4|n} phi(d). - Ridouane Oudra, Dec 31 2020 G.f.: Sum_{k>=1} phi(k) * x^(k^4) / (1 - x^(k^4)). - Ilya Gutkovskiy, Aug 20 2021 EXAMPLE a(32) = 2 since 2 = 16^(1/4) and 16 is the largest 4th power dividing 32. MAPLE A053164 := proc(n) local a, f, e, p ; for f in ifactors(n)[2] do e:= op(2, f) ; p := op(1, f) ; a := a*p^floor(e/4) ; end do ; a ; end proc: # R. J. Mathar, Jan 11 2012 MATHEMATICA f[list_] := list[[1]]^Quotient[list[[2]], 4]; Table[Apply[Times, Map[f, FactorInteger[n]]], {n, 1, 81}] (* Geoffrey Critzer, Jan 21 2015 *) PROG (Scheme, with memoization macro definec) (definec (A053164 n) (if (= 1 n) n (* (expt (A020639 n) (A002265 (A067029 n))) (A053164 (A028234 n))))) (define (A002265 n) (floor->exact (/ n 4))) ;; For MIT/GNU Scheme ;; Antti Karttunen, Sep 13 2017 CROSSREFS Cf. A000188, A000190, A008835, A053150. Sequence in context: A203640 A043289 A063775 * A295658 A307427 A318672 Adjacent sequences:  A053161 A053162 A053163 * A053165 A053166 A053167 KEYWORD nonn,mult AUTHOR Henry Bottomley, Feb 29 2000 EXTENSIONS More terms from Antti Karttunen, Sep 13 2017 STATUS approved

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Last modified July 2 13:15 EDT 2022. Contains 355007 sequences. (Running on oeis4.)