A277169 Product of squares of proper divisors of n.

1, 1, 1, 4, 1, 36, 1, 64, 9, 100, 1, 20736, 1, 196, 225, 4096, 1, 104976, 1, 160000, 441, 484, 1, 191102976, 25, 676, 729, 614656, 1, 729000000, 1, 1048576, 1089, 1156, 1225, 78364164096, 1, 1444, 1521, 4096000000, 1, 5489031744, 1, 3748096, 4100625, 2116, 1, 28179280429056, 49, 6250000

Offset

1,4

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Divisor Product

Eric Weisstein's World of Mathematics, Proper divisors

Formula

a(n) = n^(sigma_0(n)-2).

a(n) = n^A000005(n)/A000290(n).

a(n) = A000290(A007956(n))/A000290(n).

a(n) = A000290(A007955(n)/n)/A000290(n).

a(n) = A062758(n)/A000290(n).

a(n) = 1 if n is prime or n = 1 (A008578).

a(n) = n if n is square of prime (A001248).

a(n) = n^2 if n is multiplicatively perfect number (A007422).

Example

a(6) = 36 because 6 has 3 proper divisors {1,2,3} and 1^2*2^2*3^2 = 36.

Maple

seq(n^(numtheory:-tau(n)-2), n=1..50); # Robert Israel, Nov 13 2016

Mathematica

Table[n^(DivisorSigma[0, n] - 2), {n, 1, 50}]

Crossrefs

Cf. A000290, A001248, A007422, A007955, A007956, A008578, A062758.

Sequence in context: A374258 A075804 A059844 * A144284 A144285 A292442

Adjacent sequences: A277166 A277167 A277168 * A277170 A277171 A277172

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Oct 19 2016

Status

approved