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A045976 A product related to n-th roots of 1. 0
1, 1, 0, 9, 121, 2704, 118336, 4092529, 0, 97734390625, 69057113823721, 61675735716000000, 120510849036513735801, 204044070747203744272384, 0, 12086640655039701533948077217761, 424809992547069296975659357323606889 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

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

REFERENCES

related work:

(a) Dickson's  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.

(b) Idem (a), but page 757, lines 14 to 24:

Some related work of G. B. Mathews (in 1895) is described.

(c) Mathews ' work  cited in (b) appears (in French)

in page 132, lines 1 to 13 of R Nogues, Theoreme de Fermat

Son Histoire, reprint (1992) Jacques Gabay's edition of the original of 1932.

All this is related to "the first case" of Fermat's Theorem

as worked by mathematicians at the end of 19th century.

LINKS

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

FORMULA

a(n) = product ((1+u)^n +1), where u^n = 1, u != 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: A050353 A112941 A258380 * A276256 A276095 A053889

Adjacent sequences:  A045973 A045974 A045975 * A045977 A045978 A045979

KEYWORD

nonn

AUTHOR

Luis H. Gallardo

STATUS

approved

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Last modified August 3 11:20 EDT 2021. Contains 346435 sequences. (Running on oeis4.)