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A072480 Shadow transform of factorials A000142. 2
0, 1, 0, 0, 0, 0, 3, 0, 4, 3, 5, 0, 8, 0, 7, 10, 10, 0, 12, 0, 15, 14, 11, 0, 20, 15, 13, 18, 21, 0, 25, 0, 24, 22, 17, 28, 30, 0, 19, 26, 35, 0, 35, 0, 33, 39, 23, 0, 42, 35, 40, 34, 39, 0, 45, 44, 49, 38, 29, 0, 55, 0, 31, 56, 56, 52, 55, 0, 51, 46, 63, 0, 66, 0, 37, 65, 57, 66, 65 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

For n>1, the number of solutions (n,k) of k!=n! (mod n), where 1<=k<n.  [from Clark Kimberling, Feb 11 2012]

LINKS

Table of n, a(n) for n=0..78.

N. J. A. Sloane, Transforms

FORMULA

a(n)=n-A002034(n).

MATHEMATICA

s[k_] := k!;

f[n_, k_] := If[Mod[s[n] - s[k], n] == 0, 1, 0];

t[n_] := Flatten[Table[f[n, k], {k, 1, n - 1}]]

a[n_] := Count[Flatten[t[n]], 1]

Table[a[n], {n, 2, 420}] (* A072480 *)

Flatten[Position[%, 0]]  (* A006093, primes-1 *)

(* Agrees with A072480 for n>1, from Clark Kimberling, Feb 12 2012 *)

CROSSREFS

Sequence in context: A245907 A104686 A104514 * A243920 A181839 A100939

Adjacent sequences:  A072477 A072478 A072479 * A072481 A072482 A072483

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane and Vladeta Jovovic, Aug 02 2002

STATUS

approved

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Last modified February 21 07:18 EST 2018. Contains 299390 sequences. (Running on oeis4.)