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A061389 Number of (1+phi)-divisors of n. 7
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 (list; graph; refs; listen; history; text; internal format)
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: A098219 A173439 A322483 * A138011 A036555 A046927

Adjacent sequences:  A061386 A061387 A061388 * A061390 A061391 A061392

KEYWORD

nonn,mult

AUTHOR

Vladeta Jovovic, Apr 29 2001

STATUS

approved

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Last modified September 27 07:28 EDT 2021. Contains 347673 sequences. (Running on oeis4.)