OFFSET
1,4
COMMENTS
The quotient T(n,k) = (k^n - k^(n-phi(n)))/n results from the generalization k^n == k^(n-phi(n)) (mod n) of Euler's theorem (see Sierpiński, p. 243).
The n-th row of the table is equal to the n-th row of A074650 iff n = p^j (p prime, j>=1).
REFERENCES
W. Sierpiński, Elementary Theory of Numbers, Warszawa, 1964.
FORMULA
T(n,k) = (k^n - k^(n - phi(n)))/n.
EXAMPLE
T(4,3) = (3^4 - 3^2)/4 = 18.
Square array starts:
0, 1, 2, 3, 4, 5, ...
0, 1, 3, 6, 10, 15, ...
0, 2, 8, 20, 40, 70, ...
0, 3, 18, 60, 150, 315, ...
0, 6, 48, 204, 624, 1554, ...
0, 8, 108, 640, 2500, 7560, ...
MAPLE
with(numtheory):
T:= proc(n, k) (k^n-k^(n-phi(n)))/n end:
seq(seq(T(i, 1+d-i), i=1..d), d=1..11);
PROG
(PARI) T(n, k) = (k^n - k^(n - eulerphi(n)))/n; \\ Jinyuan Wang, Aug 28 2021
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Franz Vrabec, Aug 26 2021
EXTENSIONS
More terms from Jinyuan Wang, Aug 28 2021
STATUS
approved