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 A028234 If n = p_1^e_1 * ... * p_k^e_k, p_1 < ... < p_k primes, then a(n) = n/p_1^e_1, with a(1) = 1. 146
 1, 1, 1, 1, 1, 3, 1, 1, 1, 5, 1, 3, 1, 7, 5, 1, 1, 9, 1, 5, 7, 11, 1, 3, 1, 13, 1, 7, 1, 15, 1, 1, 11, 17, 7, 9, 1, 19, 13, 5, 1, 21, 1, 11, 5, 23, 1, 3, 1, 25, 17, 13, 1, 27, 11, 7, 19, 29, 1, 15, 1, 31, 7, 1, 13, 33, 1, 17, 23, 35, 1, 9, 1, 37, 25, 19, 11, 39, 1, 5, 1, 41, 1, 21 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS Together with A067029 is useful for defining sequences that are multiplicative with a(p^e) = f(e), as recurrences of the form: a(1) = 1 and for n > 1, a(n) = f(A067029(n)) * a(A028234(n)). - Antti Karttunen, May 29 2017 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA a(n) = n / A028233(n). A001221(a(n)) = A001221(n)-1; A001222(a(n)) = A001222(n)-A067029(n). - Reinhard Zumkeller, May 13 2006 MATHEMATICA a[n_] := n / Power @@ First[FactorInteger[n]]; Table[a[n], {n, 1, 84}] (* Jean-François Alcover, Jun 12 2012 *) PROG (Haskell) a028234 n = n `div` a028233 n  -- Reinhard Zumkeller, Mar 27 2013 (PARI) a(n) = {my(f = factor(n)); if (#f~, f[1, 1] = 1); factorback(f); } \\ Michel Marcus, Feb 11 2016 (Python) from sympy import factorint def a(n):     f = factorint(n)     return 1 if n==1 else n/(min(f)**f[min(f)]) # Indranil Ghosh, May 12 2017 (Scheme) (define (A028234 n) (/ n (A028233 n))) ;; Needs also code from A020639 and A028233. - Antti Karttunen, May 29 2017 (GAP) a := List(List(List(List([1..10^3], Factors), Collected), i -> i), j -> j^j);; A028234 := List([1..Length(a)], i->i/a[i]); # Muniru A Asiru, Jan 27 2018 CROSSREFS Cf. A020639, A028233, A067029. Sequence in context: A226040 A302034 A302044 * A322995 A052125 A214874 Adjacent sequences:  A028231 A028232 A028233 * A028235 A028236 A028237 KEYWORD nonn,nice,easy AUTHOR EXTENSIONS Edited name to include a(1) = 1 by Franklin T. Adams-Watters, Jan 27 2018 STATUS approved

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Last modified April 1 05:04 EDT 2020. Contains 333155 sequences. (Running on oeis4.)