login
A061389
Number of (1+phi)-divisors of n.
8
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
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
KEYWORD
nonn,mult
AUTHOR
Vladeta Jovovic, Apr 29 2001
STATUS
approved