A045976 A product related to n-th roots of 1.

1, 1, 0, 9, 121, 2704, 118336, 4092529, 0, 97734390625, 69057113823721, 61675735716000000, 120510849036513735801, 204044070747203744272384, 0, 12086640655039701533948077217761, 424809992547069296975659357323606889

Offset

1,4

Comments

a(3*(2*k+1)) = 0 for all k because there are some 3rd roots involved.

References

Related works addressing "the first case" of Fermat's Theorem as studied by mathematicians at the end of the 19th century:

L. D. Dickson, History of the Theory of Numbers, Vol II, page 756, lines -5 to -1, and page 757, lines 1 to 4: Some related work of E. Wendt is described.

L. D. Dickson, History of the Theory of Numbers, Vol II, page 757, lines 14 to 24: Some related work of G. B. Mathews (in 1895) is described.

R. Nogues, Théorème de Fermat Son Histoire (in French), reprint (1992) Jacques Gabay's edition of the original of 1932, page 132, lines 1 to 13 for G. B. Mathews's work, cited in the second Dickson reference above.

Links

Table of n, a(n) for n=1..17.

Formula

a(n) = Product_{u^n=1, u != 1} ((1+u)^n + 1).

Prog

(PARI) a(n)=sum(k=1, n-1, (1+exp(2*Pi*I/n))^n+1) \\ Charles R Greathouse IV, May 13 2011

Crossrefs

Sequence in context: A352119 A258380 A360547 * A276256 A276095 A053889

Adjacent sequences: A045973 A045974 A045975 * A045977 A045978 A045979

Keyword

nonn

Author

Luis H. Gallardo

Status

approved