|
| |
|
|
A069118
|
|
Let D(n,s) denotes the denominator of Sum_{k=1..n} 1/k^s; sequence gives values of n such that D(n,4)/D(n,2) is a perfect square.
|
|
1
|
|
|
|
1, 2, 3, 4, 5, 6, 7, 8, 9, 15, 16, 17, 18, 19, 28, 29, 30, 31, 32, 33, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
3 is in the sequence because 1/1^4 +1/2^4 + 1/3^4 = 1393/1296 and 1/1^2 + 1/2^2 + 1/3^2 = 49/36, and 1296/36 = 36 = 6^2.
|
|
|
MAPLE
|
dd:= (n, s) -> denom(add(1/k^s, k=1..n)):
select(t -> issqr(dd(t, 4)/dd(t, 2)), [$1..1000]); # Robert Israel, May 18 2014
|
|
|
PROG
|
(PARI) default(realprecision, 1000); for(n=1, 300, if(sqrt(denominator(sum(i=1, n, 1/i^4))/denominator(sum(i=1, n, 1/i^2))) == floor(sqrt(denominator(sum(i=1, n, 1/i^4))/denominator(sum(i=1, n, 1/i^2)))), print1(n, ", ")))
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
easy,nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
