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%I #32 Feb 26 2024 01:25:22
%S 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,
%T 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,
%U 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
%N 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.
%C 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
%H Reinhard Zumkeller, <a href="/A049599/b049599.txt">Table of n, a(n) for n = 1..10000</a>
%F 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
%t 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 *)
%o (Haskell)
%o a049599 = product . map ((+ 1) . a000005 . fromIntegral) . a124010_row
%o -- _Reinhard Zumkeller_, Mar 13 2012
%o (PARI) a(n) = vecprod(apply(x->numdiv(x)+1, factor(n)[, 2])); \\ _Amiram Eldar_, Aug 13 2023
%Y Cf. A049603, A051378.
%Y Cf. A124010, A000005, A049419, A077610, A322791.
%K nonn,easy,nice,mult
%O 1,2
%A _Yasutoshi Kohmoto_
%E More terms from _Naohiro Nomoto_, Apr 12 2001
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