A290641 Multiplicative with a(p^e) = prime(p-1)^e.

1, 2, 3, 4, 7, 6, 13, 8, 9, 14, 29, 12, 37, 26, 21, 16, 53, 18, 61, 28, 39, 58, 79, 24, 49, 74, 27, 52, 107, 42, 113, 32, 87, 106, 91, 36, 151, 122, 111, 56, 173, 78, 181, 116, 63, 158, 199, 48, 169, 98, 159, 148, 239, 54, 203, 104, 183, 214, 271, 84, 281, 226, 117, 64, 259

Offset: 1

Author

Michel Marcus, Aug 08 2017

Keywords

• nonn
• mult

Comments

a(n) = A064554(n) for 1 <= n < 91, but a(91) = 481 differs from A064554(91) = 463. - Georg Fischer, Oct 23 2018

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A046523, A055003, A064554, A064988, A064989.

Programs

Mathematica

Array[If[# == 1, 1, Times @@ Map[Prime[#1 - 1]^#2 & @@ # &, FactorInteger[#]]] &, 65] (* Michael De Vlieger, Apr 22 2021 *)

PARI

a(n) = {my(f = factor(n)); for (k=1, #f~, f[k, 1] = prime(f[k, 1]-1);); factorback(f);}

Python

from sympy import factorint, prime
from operator import mul
from functools import reduce
def a(n):
    return 1 if n==1 else reduce(mul, [prime(p - 1)**e for p, e in factorint(n).items()])
print([a(n) for n in range(1, 101)]) # Indranil Ghosh, Aug 08 2017

Scheme

(define (A290641 n) (if (= 1 n) n (* (A000040 (+ -1 (A020639 n))) (A290641 (A032742 n))))) ;; Antti Karttunen, Aug 08 2017

Formula

From Antti Karttunen, Aug 08 2017: (Start)

a(n) = A064989(A064988(n)).

A046523(a(n)) = A046523(n). [Preserves the prime signature of n].

(End)