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, 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

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..3952

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

Sequence in context: A073526 A032992 A190298 * A328933 A032978 A197181

Adjacent sequences: A069115 A069116 A069117 * A069119 A069120 A069121

Keyword

easy,nonn

Author

Benoit Cloitre, Apr 07 2002

Status

approved