A351462 Multiplicative, with a(p^k) = a(p^k-1) + 2 for any k > 0 and p prime.

1, 3, 5, 7, 9, 15, 17, 19, 21, 27, 29, 35, 37, 51, 45, 47, 49, 63, 65, 63, 85, 87, 89, 95, 97, 111, 113, 119, 121, 135, 137, 139, 145, 147, 153, 147, 149, 195, 185, 171, 173, 255, 257, 203, 189, 267, 269, 235, 237, 291, 245, 259, 261, 339, 261, 323, 325, 363

Offset

1,2

Comments

All terms are odd.

Changing the parameter "2" in the name to:

- 0 gives the all 1's sequence (A000012),

- 1 gives the positive integers (A000027),

- -2 gives A351463.

Links

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

Rémy Sigrist, Scatterplot of the first 100000 terms

Example

a(1) = 1 (as this sequence is multiplicative).
a(2) = a(1) + 2 = 3.
a(3) = a(2) + 2 = 5.
a(7) = a(6) + 2 = a(2)*a(3) + 2 = 17.
a(42) = a(2)*a(3)*a(7) = 255.

Maple

a:= proc(n) option remember;
      mul(a(i[1]^i[2]-1)+2, i=ifactors(n)[2])
    end:
seq(a(n), n=1..58);  # Alois P. Heinz, Feb 13 2022

Mathematica

a[n_] := a[n] = If[n == 1, 1,
     Product[{p, k} = pk; a[p^k-1]+2, {pk, FactorInteger[n]}]];
Table[a[n], {n, 1, 58}] (* Jean-François Alcover, May 08 2022 *)

Prog

(PARI) a(n) = { my (f=factor(n)); if (#f~==1, a(n-1)+2, prod (k=1, #f~, a(f[k, 1]^f[k, 2]))) }
(Python)
from math import prod
from sympy import factorint
from functools import cache
@cache
def a(n):
    if n == 1: return 1
    return prod(a(p**k-1)+2 for p, k in factorint(n).items())
print([a(n) for n in range(1, 59)]) # Michael S. Branicky, Feb 13 2022

Crossrefs

Cf. A000012, A000027, A351463.

Sequence in context: A268496 A121820 A357150 * A258159 A238257 A305409

Adjacent sequences: A351459 A351460 A351461 * A351463 A351464 A351465

Keyword

nonn,look,mult

Author

Rémy Sigrist, Feb 11 2022

Status

approved