

A076619


Least x>1 such that x^d == 1 (mod d) for each divisor d of n, for all nonsquarefree numbers n (cf. A013929).


0



3, 3, 4, 7, 3, 7, 11, 7, 6, 4, 15, 3, 7, 11, 23, 16, 7, 8, 11, 27, 7, 15, 31, 22, 3, 35, 7, 16, 39, 11, 4, 43, 23, 31, 47, 7, 15, 34, 11, 27, 7, 15, 59, 40, 31, 12, 63, 6, 43, 3, 67, 16, 35, 71, 7, 22, 75, 31, 39, 52, 79, 11, 7, 83, 43, 14, 58, 87, 36, 23, 31, 47, 95, 22, 7, 15, 67
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OFFSET

1,1


COMMENTS

If n is squarefree (cf. A005117), then the least x>1 such that x^d == 1 (mod d) (for each divisor d of n) equals n+1.


LINKS

Table of n, a(n) for n=1..77.


FORMULA

a(p^m) = p+1 for p prime and m>1.
a(n) = A076618(A013929(n)).  Michel Marcus, Jul 13 2013
a(n) = A076333(n) + 1.  Amiram Eldar, Feb 11 2021


MATHEMATICA

f[n_] := If[(r = Times @@ FactorInteger[n][[;; , 1]]) < n, r, 0]; Select[f /@ Range[200], # > 0 &] + 1 (* Amiram Eldar, Feb 11 2021 *)


PROG

(PARI) lista(nn) = {for(n=1, nn, if (!issquarefree(n), print1(A076618(n), ", "); ); ); } \\ Michel Marcus, Jul 13 2013


CROSSREFS

Cf. A013929, A076333, A076618 (sequence for all integers).
Sequence in context: A058660 A059871 A273096 * A318140 A266025 A216626
Adjacent sequences: A076616 A076617 A076618 * A076620 A076621 A076622


KEYWORD

nonn


AUTHOR

Benoit Cloitre, Oct 22 2002


STATUS

approved



