A061389 Number of (1+phi)-divisors of n.

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, 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, 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

Offset: 1

Author

Vladeta Jovovic, Apr 29 2001

Keywords

• nonn
• mult

Comments

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.

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A069915, A049419, A049599.

Cf. A124010, A000010.

Programs

Haskell

a061389 = product . map ((+ 1) . a000010 . fromIntegral) . a124010_row
-- Reinhard Zumkeller, Mar 13 2012

Mathematica

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

Formula

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