%I
%S 1,1,2,1,4,2,6,1,4,4,10,2,12,6,8,1,16,4,18,4,12,10,22,2,
%T 16,12,8,6,28,8,30,1,20,16,24,4,36,18,24,4,40,12,42,10,16,
%U 22,46,2,36,16,32,12,52,8,40,6,36,28,58,8,60,30,24,1,48,20,66,16,44,24,70,4,72,36,32
%N Product 1p, where p ranges over the prime factors of n with multiplicity.
%C f(1), where f is the monic polynomial whose zeros are the prime factors of n with multiplicity.
%C a(p) = 1p for any prime number p.
%H Alois P. Heinz, <a href="/A125131/b125131.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Di#divseq">Index to divisibility sequences</a>
%F Completely multiplicative with a(p) = 1p.  _Franklin T. AdamsWatters_, Jan 17 2007
%F a(n) = f(1), where f(x)=(xp_1)(xp_2)...(xp_m), where { p_1,p_2,...p_m } are the prime factors of n with multiplicity.
%F a(n) = A003958(n) * A008836(n).
%e a(120) = 8 because the prime factorization of 120 is 2*2*2*3*5, so f(x)=(x2)(x2)(x2)(x3)(x5) and f(1)=(1)*(1)*(1)*(2)*(4)= 8.
%p a:= n> mul((1i[1])^i[2], i=ifactors(n)[2]):
%p seq(a(n), n=1..80); # _Alois P. Heinz_, Jun 28 2015
%t f[n_] := Times @@ (Flatten[Table[ #1, {#2}] & @@@ FactorInteger@n] + 1); Array[g, 80] (* _Robert G. Wilson v_, Jan 10 2007 *)
%o (?) f=polyroot(factor(x)); f(1)
%o (PARI) a(n)=my(f=factor(n)); prod(i=1,#f~,(1f[i,1])^f[i,2]) \\ _Charles R Greathouse IV_, Jun 28 2015
%Y Cf. A003958, A008836.
%K easy,sign,mult
%O 1,3
%A Mitch Cervinka (puritan(AT)toast.net), Jan 10 2007
%E Edited by _Franklin T. AdamsWatters_, Jan 17 2007
