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A277169
Product of squares of proper divisors of n.
1
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
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}]
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Oct 19 2016
STATUS
approved