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%I #24 Sep 17 2022 11:41:53
%S 1,2,3,4,5,36,7,8,9,100,11,144,13,196,225,16,17,324,19,400,441,484,23,
%T 576,25,676,27,784,29,27000,31,32,1089,1156,1225,1296,37,1444,1521,
%U 1600,41,74088,43,1936,2025,2116,47,2304,49,2500,2601,2704,53,2916
%N a(n) = n^omega(n).
%C Not always equal to product of unitary divisors of n [compare with A061537]. This deviates from A061537 at 30, 42, 60, 66, etc.
%H Harry J. Smith, <a href="/A062509/b062509.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = Sum_{d|n} tau(d^n)*mu(n/d). - _Ridouane Oudra_, Sep 17 2022
%e n=30: a(30) = 30^3 = 27000;
%e n=72: a(72) = 72^2 = 5184.
%t Table[n^PrimeNu[n],{n,60}] (* _Harvey P. Dale_, Jan 14 2013 *)
%o (PARI) a(n)={n^omega(n)} \\ _Harry J. Smith_, Aug 08 2009
%o (Haskell)
%o a062509 n = n ^ a001221 n -- _Reinhard Zumkeller_, Sep 13 2013
%Y Cf. A001221, A061537, A034444, A000005, A033992.
%Y Cf. A176029, A229109.
%K nonn
%O 1,2
%A _Labos Elemer_, Jul 13 2001
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