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 A053165 4th-power-free part of n. 11
 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 2, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 3, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 4, 65, 66, 67, 68, 69, 70, 71, 72, 73 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Chai Wah Wu, Table of n, a(n) for n = 1..10000 Henry Bottomley, Some Smarandache-type multiplicative sequences. FORMULA a(n) = n/A008835(n). Dirichlet g.f.: zeta(4s)*zeta(s-1)/zeta(4s-4). The Dirichlet convolution of this sequence with A008835 is A000203. - R. J. Mathar, Apr 05 2011 From Peter Munn, Jan 15 2020: (Start) a(2) = 2; a(4) = 4; a(n^4) = 1; a(A003961(n)) = A003961(a(n)); a(A059897(n,k)) = A059897(a(n), a(k)). a(A225546(n)) = A225546(A065331(n)). (End) Multiplicative with a(p^e) = p^(e mod 4). - Amiram Eldar, Sep 07 2020 MATHEMATICA f[p_, e_] := p^Mod[e, 4]; a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Sep 07 2020 *) PROG (Python) from operator import mul from functools import reduce from sympy import factorint def A053165(n):     return 1 if n <=1 else reduce(mul, [p**(e % 4) for p, e in factorint(n).items()]) # Chai Wah Wu, Feb 04 2015 (PARI) a(n)=my(f=factor(n)); f[, 2]=f[, 2]%4; factorback(f) \\ Charles R Greathouse IV, Sep 02 2015 CROSSREFS Equivalent sequences for other powers: A007913 (2), A050985 (3). Cf. A000190, A000203, A008835. A003961, A059897 are used to express relationship between terms of this sequence. Related to A065331 via A225546. Sequence in context: A002377 A053836 A025483 * A056962 A043275 A216455 Adjacent sequences:  A053162 A053163 A053164 * A053166 A053167 A053168 KEYWORD nonn,mult AUTHOR Henry Bottomley, Feb 29 2000 STATUS approved

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Last modified December 5 19:53 EST 2020. Contains 338965 sequences. (Running on oeis4.)