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 A241663 Number of positive integers k less than or equal to n such that gcd(k,n) = gcd(k+1,n) = gcd(k+2,n) = gcd(k+3,n) = 1. 5
 1, 0, 0, 0, 1, 0, 3, 0, 0, 0, 7, 0, 9, 0, 0, 0, 13, 0, 15, 0, 0, 0, 19, 0, 5, 0, 0, 0, 25, 0, 27, 0, 0, 0, 3, 0, 33, 0, 0, 0, 37, 0, 39, 0, 0, 0, 43, 0, 21, 0, 0, 0, 49, 0, 7, 0, 0, 0, 55, 0, 57, 0, 0, 0, 9, 0, 63, 0, 0, 0, 67, 0, 69, 0, 0, 0, 21, 0, 75, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 COMMENTS a(n) is the 4th Schemmel totient function. LINKS Antti Karttunen, Table of n, a(n) for n = 1..16384 C. Defant, On Arithmetic Functions Related to Iterates of the Schemmel Totient Functions, J. Int. Seq. 18 (2015) # 15.2.1 Nittiya Pabhapote and Vichian Laohakosol, Combinatorial Aspects of the Generalized Euler's Totient, International Journal of Mathematics and Mathematical Sciences, Volume 2010 (2010), Article ID 648165, 15 p. FORMULA Multiplicative with a(p^e) = p^(e-1)*(p-4) for p > 3. a(2^e) = a(3^e) = 0 for e > 0. EXAMPLE a(35) = a(5)*a(7) = 1*3 = 3. MATHEMATICA Table[Boole[n == 1] + Count[Partition[Range@ n, 4, 1], _?(AllTrue[#, CoprimeQ[n, #] &] &)], {n, 81}] (* or *) Array[If[# == 1, 1, Apply[Times, FactorInteger[#] /. {p_, e_} /; p > 1 :> If[p > 3, (p - 4) p^(e - 1), 0]]] &, 81] (* Michael De Vlieger, Nov 05 2017 *) PROG (PARI) a(n) = {my(f = factor(n)); prod(i=1, #f~, if ((f[i, 1] == 2) || (f[i, 1] == 3), 0, f[i, 1]^(f[i, 2]-1)*(f[i, 1]-4))); } \\ Michel Marcus, May 01 2014 (Scheme) ;; After the given multiplicative formula. Uses memoization-macro definec: (definec (A241663 n) (if (= 1 n) n (let ((p (A020639 n))) (if (<= p 3) 0 (* (- p 4) (expt p (- (A067029 n) 1)) (A241663 (A028234 n))))))) ;; Antti Karttunen, Nov 05 2017 CROSSREFS Cf. A058026, A241666. Sequence in context: A160086 A115869 A115859 * A129170 A342590 A209436 Adjacent sequences:  A241660 A241661 A241662 * A241664 A241665 A241666 KEYWORD nonn,mult AUTHOR Colin Defant, Apr 26 2014 STATUS approved

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Last modified May 16 21:28 EDT 2021. Contains 343951 sequences. (Running on oeis4.)