A279510 Multiplicative with a(p(i)^j) = p(i+1)^a(j) for i-th prime p(i) and j>0.

1, 3, 5, 27, 7, 15, 11, 243, 125, 21, 13, 135, 17, 33, 35, 7625597484987, 19, 375, 23, 189, 55, 39, 29, 1215, 343, 51, 3125, 297, 31, 105, 37, 2187, 65, 57, 77, 3375, 41, 69, 85, 1701, 43, 165, 47, 351, 875, 87, 53, 38127987424935, 1331, 1029, 95, 459, 59

Offset: 1

Author

Rémy Sigrist, Dec 13 2016

Keywords

• nonn
• mult

Comments

This sequence establishes a bijection between the natural numbers and A182318.

Records: 1, 3, 5, 27, 243, 7625597484987, 38127987424935, 53379182394909, 7450580596923828125, 22351741790771484375, ..., .

Records appear at: 1, 2, 3, 4, 8, 16, 48, 80, 81, 162, 256, 768, 1280, 1792, 2304, 6400, 6561, 13122, 26244, ..., . Robert G. Wilson v, Dec 14 2016

Examples

			a(6) = a(2*3) = 3*5 = 15
a(16) = a(2^(2^2)) = 3^(3^3) = 7625597484987
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003961, A182318.

Programs

Mathematica

a[n_] := Block[{fi = FactorInteger@ n}, Times @@ (NextPrime[#[[1]]]^a[#[[2]]] & /@ fi)]; a[1] = 1; Array[a, 60] (* Robert G. Wilson v, Dec 14 2016 *)

PARI

a(n) =  my (f=factor(n)); return (prod(i=1, #f~, nextprime(1+f[i,1])^a(f[i,2])))