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

1,2

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A069915, A049419, A049599.

Cf. A124010, A000010.

Sequence in context: A173439 A372380 A322483 * A366763 A138011 A036555

Adjacent sequences: A061386 A061387 A061388 * A061390 A061391 A061392

Keyword

nonn,mult

Author

Vladeta Jovovic, Apr 29 2001

Status

approved