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^k divides n. - Charles R Greathouse IV, Aug 27 2012
EXAMPLE
From Bernard Schott, Dec 19 2021: (Start)
There are 2 groups with order 6: C_6 that is cyclic so nilpotent, and the symmetric group S_3 that is not nilpotent, hence 6 is a term.
There are also 2 groups with order 10: C_10 that is cyclic so nilpotent, and the dihedral group D_10 that is not nilpotent, hence 10 is another term. (End)
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
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