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%I #15 Jun 24 2019 04:00:57
%S 1,-2,-3,0,-5,36,-7,0,0,100,-11,0,-13,196,225,0,-17,0,-19,0,441,484,
%T -23,0,0,676,0,0,-29,810000,-31,0,1089,1156,1225,0,-37,1444,1521,0,
%U -41,3111696,-43,0,0,2116,-47,0,0,0,2601,0,-53,0,3025,0,3249,3364,-59,0,-61,3844
%N Product_{ d divides n } d*mu(n/d).
%C a(n) is the multiplicative equivalent to Euler's totient function, phi(n) = Sum_{ d divides n } d*mu(n/d).
%C a(n) = 0 iff n is not squarefree (A013929).
%C a(n) < 0 iff n is prime (A000040).
%C a(n) = -n iff n has 1 prime factor.
%C a(n) = n^(2^(k-1)) iff n has k prime factors (k>1).
%e a(14) = 1*(1)*2*(-1)*7*(-1)*14*(1) = 14^2 = 196.
%p with(numtheory): A190902 := proc(n) local d; mul(d*mobius(n/d),d=divisors(n)) end:
%p A190902 := proc(n) if mobius(n)=0 then 0 elif isprime(n) then -n else n^(2^(nops(factorset(n))-1)) fi end:
%t a[n_] := Product[d MoebiusMu[n/d], {d, Divisors[n]}];
%t Array[a, 62] (* _Jean-François Alcover_, Jun 24 2019 *)
%o (PARI) a(n)={local(r=1);fordiv(n,d,r*=d*moebius(n/d));return(r);}
%K sign
%O 1,2
%A _Peter Luschny_, Jul 22 2011
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