OFFSET
1,2
COMMENTS
Sequence is obviously infinite.
If the sequence is restricted to only prime n's, the sequence increases absolutely. See comment in A083503.
[Since there is actually no comment in A083503: this probably means to say that (conjectural!) A083503(prime(n)) = A008864(n) which leads to a(p) = Sum_{s=2..p} binomial(p,s)*p^(s-1) for primes p, an increasing subsequence. - R. J. Mathar, Aug 01 2025]
a(n) = (x^n-1)/n - n, where x is the least integer > 1 with x^n == 1 (mod n). - Robert Israel, Aug 01 2025
LINKS
Robert Israel, Table of n, a(n) for n = 1..388
MAPLE
A083502 := proc(n)
local a, b ;
if n = 1 then
1 ;
else
for b from 2 do
a := (b^n-1)/n-n ;
if type( a, 'integer') then
return a;
end if;
end do:
end if;
end proc:
seq(A083502(n), n=1..20) ; # R. J. Mathar, Aug 01 2025
# Alternative:
f:= proc(n) local X, S;
S:= min(map(t -> subs(t, X), {msolve(X^n = 1, n)} minus {{X=1}}));
if S = infinity then ((n+1)^n - 1)/n - n else (S^n-1)/n - n fi
end proc:
f(1):= 1:
map(f, [$1..50]); # Robert Israel, Aug 01 2025
MATHEMATICA
Do[i = 2; While[k = (i^n - 1)/n - n; !IntegerQ[k], i++ ]; Print[k], {n, 1, 20}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 03 2003
EXTENSIONS
Edited and extended by Robert G. Wilson v, May 11 2003
STATUS
approved