

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
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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, AugustSeptember 2000, pp. 631634.


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[#]& ] (* JeanFrançois 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]^j1)>1, return(1)))); 0 \\ Charles R Greathouse IV, Sep 18 2012
(Haskell)
a056868 n = a056868_list !! (n1)
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



