A301315 Multiplicative with a(p^e) = prime(p) ^ a(e) (where prime(k) denotes the k-th prime number).

1, 3, 5, 27, 11, 15, 17, 243, 125, 33, 31, 135, 41, 51, 55, 7625597484987, 59, 375, 67, 297, 85, 93, 83, 1215, 1331, 123, 3125, 459, 109, 165, 127, 177147, 155, 177, 187, 3375, 157, 201, 205, 2673, 179, 255, 191, 837, 1375, 249, 211, 38127987424935, 4913, 3993

Offset: 1

Author

Rémy Sigrist, Mar 18 2018

Keywords

• nonn
• mult

Comments

This sequence is a recursive version of A064988.

This sequence is injective (all terms are distinct).

Links

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

Crossrefs

Cf. A064988, A225395, A279690.

Programs

Mathematica

Fold[Function[{a, n}, Append[a, Times @@ Map[Prime[#1]^a[[#2]] & @@ # &, FactorInteger@ n]]], {1}, Range[2, 50]] (* Michael De Vlieger, Mar 19 2018 *)

PARI

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

Formula

A225395(a(n)) = n.

A279690(a(n)) = A279690(n).