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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. 4
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 A209436 A229121

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 February 24 10:11 EST 2020. Contains 332209 sequences. (Running on oeis4.)