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A056868 Numbers that are not nilpotent numbers. 15
6, 10, 12, 14, 18, 20, 21, 22, 24, 26, 28, 30, 34, 36, 38, 39, 40, 42, 44, 46, 48, 50, 52, 54, 55, 56, 57, 58, 60, 62, 63, 66, 68, 70, 72, 74, 75, 76, 78, 80, 82, 84, 86, 88, 90, 92, 93, 94, 96, 98, 100, 102, 104, 105, 106, 108, 110, 111, 112, 114, 116, 117, 118, 120 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A number is nilpotent if every group of order n is nilpotent.

The sequence "Numbers of the form (k*i + 1)*k*j with i, j >= 1 and k >= 2" agrees with this for the first 146 terms but then differs. Cf. A300737. - Gionata Neri, Mar 11 2018

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

J. Pakianathan and K. Shankar, Nilpotent Numbers, Amer. Math. Monthly, 107, August-September 2000, pp. 631-634.

FORMULA

n is in this sequence if p^k = 1 mod q for primes p and q dividing n such that p^e but not p^(e+1) divides n and k <= e. - Charles R Greathouse IV, Aug 27 2012

MATHEMATICA

nilpotentQ[n_] := With[{f = FactorInteger[n]}, Sum[ Boole[ Mod[p[[1]]^p[[2]], q[[1]]] == 1], {p, f}, {q, f}]] == 0; Select[ Range[120], !nilpotentQ[#]& ] (* Jean-François Alcover, Sep 03 2012 *)

PROG

(PARI) is(n)=my(f=factor(n)); for(k=1, #f[, 1], for(j=1, f[k, 2], if(gcd(n, f[k, 1]^j-1)>1, return(1)))); 0 \\ Charles R Greathouse IV, Sep 18 2012

(Haskell)

a056868 n = a056868_list !! (n-1)

a056868_list = filter (any (== 1) . pks) [1..] where

   pks x = [p ^ k `mod` q | let fs = a027748_row x, q <- fs,

                            (p, e) <- zip fs $ a124010_row x, k <- [1..e]]

-- Reinhard Zumkeller, Jun 28 2013

CROSSREFS

Complement of A056867.

Subsequence of A060652; A068919 is a subsequence.

Cf. A003277, A051532, A056866, A027748, A124010, A300737.

Sequence in context: A050703 A135711 A161543 * A069209 A060702 A054741

Adjacent sequences:  A056865 A056866 A056867 * A056869 A056870 A056871

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane, Sep 02 2000

EXTENSIONS

More terms from Francisco Salinas (franciscodesalinas(AT)hotmail.com), Dec 25 2001

STATUS

approved

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Last modified September 25 01:17 EDT 2018. Contains 315360 sequences. (Running on oeis4.)