|
|
A300905
|
|
a(n) = n^sigma(n) mod sigma(n)^n.
|
|
1
|
|
|
0, 8, 17, 1978, 73, 0, 1570497, 1009588832, 7390478182, 1391503283200, 166394893969, 151448237549551616, 762517292682713, 18685202394240778240, 814227337406354049, 187036938412352867328077, 947615093635545799201, 2095989269871299377743863001
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
sigma(n) = the sum of the divisors of n (A000203).
n^sigma(n) > sigma(n)^n for all n > 2.
|
|
LINKS
|
|
|
FORMULA
|
If n is a k-perfect number from A007691, then a(n) = 0 iff k divides n.
|
|
EXAMPLE
|
For n = 6; a(6) = 0 because 6^sigma(6) mod sigma(6)^6 = 6^12 mod 12^6 = 2176782336 mod 2985984 = 0.
|
|
MAPLE
|
with(numtheory): seq(n &^ sigma(n) mod sigma(n)^n, n=1..20); # Muniru A Asiru, Mar 20 2018
|
|
MATHEMATICA
|
Array[With[{s = DivisorSigma[1, #]}, PowerMod[#, s, s^#]] &, 18] (* Michael De Vlieger, Mar 16 2018 *)
|
|
PROG
|
(Magma) [n^SumOfDivisors(n) mod SumOfDivisors(n)^n: n in[1..20]]
(PARI) a(n) = my(s=sigma(n)); lift(Mod(n, s^n)^s); \\ Michel Marcus, Mar 17 2018
(GAP) List([1..20], n->PowerModInt(n, Sigma(n), Sigma(n)^n))); # Muniru A Asiru, Mar 20 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|