cp's OEIS Frontend

A277169 Product of squares of proper divisors of n.

%I A277169 #25 Feb 16 2025 08:33:36
%S A277169 1,1,1,4,1,36,1,64,9,100,1,20736,1,196,225,4096,1,104976,1,160000,441,
%T A277169 484,1,191102976,25,676,729,614656,1,729000000,1,1048576,1089,1156,
%U A277169 1225,78364164096,1,1444,1521,4096000000,1,5489031744,1,3748096,4100625,2116,1,28179280429056,49,6250000
%N A277169 Product of squares of proper divisors of n.
%H A277169 Robert Israel, <a href="/A277169/b277169.txt">Table of n, a(n) for n = 1..10000</a>
%H A277169 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DivisorProduct.html">Divisor Product</a>
%H A277169 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ProperDivisor.html">Proper divisors</a>
%F A277169 a(n) = n^(sigma_0(n)-2).
%F A277169 a(n) = n^A000005(n)/A000290(n).
%F A277169 a(n) = A000290(A007956(n))/A000290(n).
%F A277169 a(n) = A000290(A007955(n)/n)/A000290(n).
%F A277169 a(n) = A062758(n)/A000290(n).
%F A277169 a(n) = 1 if n is prime or n = 1 (A008578).
%F A277169 a(n) = n if n is square of prime (A001248).
%F A277169 a(n) = n^2 if n is multiplicatively perfect number (A007422).
%e A277169 a(6) = 36 because 6 has 3 proper divisors {1,2,3} and 1^2*2^2*3^2 = 36.
%p A277169 seq(n^(numtheory:-tau(n)-2), n=1..50); # _Robert Israel_, Nov 13 2016
%t A277169 Table[n^(DivisorSigma[0, n] - 2), {n, 1, 50}]
%Y A277169 Cf. A000290, A001248, A007422, A007955, A007956, A008578, A062758.
%K A277169 nonn,easy
%O A277169 1,4
%A A277169 _Ilya Gutkovskiy_, Oct 19 2016