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 A091050 Number of divisors of n that are perfect powers. 22
 1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 4, 1, 2, 1, 2, 1, 1, 1, 3, 2, 1, 3, 2, 1, 1, 1, 5, 1, 1, 1, 4, 1, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 4, 2, 2, 1, 2, 1, 3, 1, 3, 1, 1, 1, 2, 1, 1, 2, 6, 1, 1, 1, 2, 1, 1, 1, 5, 1, 1, 2, 2, 1, 1, 1, 4, 4, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 2, 1, 1, 1, 5, 1, 2, 2, 4, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS a(n)=1 iff n is squarefree: a(A005117(n))=1, a(A013929(n))>1; a(p^k)=k for p prime, k>0: a(A000961(n))=A025474(n); not the same as A005361: a(72)=5 <> A005361(72)=6. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Perfect Power Eric Weisstein's World of Mathematics, Divisor Function FORMULA a(n) = A073093(n)-A001221(n) = A001222(n)-A001221(n)+1. - David W. Wilson, Aug 28 2007 a(n) = sum (A075802(A027750(n,k)): k=1..A000005(n)). - Reinhard Zumkeller, Dec 13 2012 G.f.: Sum_{k=i^j, i>=1, j>=2, excluding duplicates} x^k/(1 - x^k). - Ilya Gutkovskiy, Mar 20 2017 EXAMPLE Divisors of n=108: {1,2,3,4,6,9,12,18,27,36,54,108}, a(108) = #{1^2, 2^2, 3^2, 3^3, 6^2} = 5. MATHEMATICA ppQ[n_] := GCD @@ Last /@ FactorInteger@ n > 1; ppQ[1] = True; f[n_] := Length@ Select[ Divisors@ n, ppQ]; Array[f, 105] (* Robert G. Wilson v, Dec 12 2012 *) PROG (Haskell) a091050 = sum . map a075802 . a027750_row -- Reinhard Zumkeller, Dec 13 2012 (PARI) a(n) = 1+ sumdiv(n, d, ispower(d)>1); \\ Michel Marcus, Sep 21 2014 CROSSREFS Cf. A091051, A001597, A000005. Sequence in context: A072411 A290107 A212180 * A005361 A303915 A322885 Adjacent sequences:  A091047 A091048 A091049 * A091051 A091052 A091053 KEYWORD nonn AUTHOR Reinhard Zumkeller, Dec 15 2003 STATUS approved

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Last modified October 21 21:44 EDT 2019. Contains 328315 sequences. (Running on oeis4.)