A049599 Number of (1+e)-divisors of n: if n = Product p(i)^r(i), d = Product p(i)^s(i) and s(i) = 0 or s(i) divides r(i), then d is a (1+e)-divisor of n.

1, 2, 2, 3, 2, 4, 2, 3, 3, 4, 2, 6, 2, 4, 4, 4, 2, 6, 2, 6, 4, 4, 2, 6, 3, 4, 3, 6, 2, 8, 2, 3, 4, 4, 4, 9, 2, 4, 4, 6, 2, 8, 2, 6, 6, 4, 2, 8, 3, 6, 4, 6, 2, 6, 4, 6, 4, 4, 2, 12, 2, 4, 6, 5, 4, 8, 2, 6, 4, 8, 2, 9, 2, 4, 6, 6, 4, 8, 2, 8, 4, 4, 2, 12, 4, 4, 4, 6, 2, 12, 4, 6, 4, 4, 4, 6, 2, 6, 6, 9, 2, 8, 2

Offset

1,2

Comments

A divisor of n is a (1+e)-divisor if and only if it is a unitary divisor of an exponential divisor of n (see A077610 and A322791). - Amiram Eldar, Feb 26 2024

Links

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

Formula

If n = Product p(i)^r(i) then a(n) = Product (tau(r(i))+1), where tau(n) = number of divisors of n, cf. A000005. - Vladeta Jovovic, Apr 29 2001

Mathematica

a[n_] := Times @@ (DivisorSigma[0, #] + 1 &)  /@ FactorInteger[n][[All, 2]]; a[1] = 1; Table[a[n], {n, 1, 103}] (* Jean-François Alcover, Oct 10 2011 *)

Prog

(Haskell)
a049599 = product . map ((+ 1) . a000005 . fromIntegral) . a124010_row
-- Reinhard Zumkeller, Mar 13 2012
(PARI) a(n) = vecprod(apply(x->numdiv(x)+1, factor(n)[, 2])); \\ Amiram Eldar, Aug 13 2023

Crossrefs

Cf. A049603, A051378.

Cf. A124010, A000005, A049419, A077610, A322791.

Sequence in context: A377519 A073182 A282446 * A353898 A366901 A365551

Adjacent sequences: A049596 A049597 A049598 * A049600 A049601 A049602

Keyword

nonn,easy,nice,mult

Author

Yasutoshi Kohmoto

Extensions

More terms from Naohiro Nomoto, Apr 12 2001

Status

approved