A061389 - OEIS

%I #13 Aug 30 2019 04:17:10

%S 1,2,2,2,2,4,2,3,2,4,2,4,2,4,4,3,2,4,2,4,4,4,2,6,2,4,3,4,2,8,2,5,4,4,

%T 4,4,2,4,4,6,2,8,2,4,4,4,2,6,2,4,4,4,2,6,4,6,4,4,2,8,2,4,4,3,4,8,2,4,

%U 4,8,2,6,2,4,4,4,4,8,2,6,3,4,2,8,4,4,4,6,2,8,4,4,4,4,4,10,2,4,4,4,2,8,2,6

%N Number of (1+phi)-divisors of n.

%C d is called a (1+phi)-divisor of a number n with prime factorization n = Product p(i)^r(i) if d|n and d = Product p(i)^s(i), where s(i)=0 or GCD(s(i),r(i))=1.

%C a(n) is odd iff n is a 3-full number (cf. A036966).

%H Reinhard Zumkeller, <a href="/A061389/b061389.txt">Table of n, a(n) for n = 1..10000</a>

%F Multiplicative with a(p^e) = A000010(e)+1.

%t f[p_, e_] := EulerPhi[e] + 1; a[1] = 1; a[n_] := Times @@ ( f @@@ FactorInteger[n] ); Array[a, 100] (* _Amiram Eldar_, Aug 30 2019*)

%o (Haskell)

%o a061389 = product . map ((+ 1) . a000010 . fromIntegral) . a124010_row

%o -- _Reinhard Zumkeller_, Mar 13 2012

%Y Cf. A069915, A049419, A049599.

%Y Cf. A124010, A000010.

%K nonn,mult

%O 1,2

%A _Vladeta Jovovic_, Apr 29 2001