A071786 In prime factorization of n replace each prime with its reversal (in decimal notation).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 31, 14, 15, 16, 71, 18, 91, 20, 21, 22, 32, 24, 25, 62, 27, 28, 92, 30, 13, 32, 33, 142, 35, 36, 73, 182, 93, 40, 14, 42, 34, 44, 45, 64, 74, 48, 49, 50, 213, 124, 35, 54, 55, 56, 273, 184, 95, 60, 16, 26, 63, 64, 155, 66, 76, 284, 96, 70, 17, 72

Offset: 1

Author

Reinhard Zumkeller, Jun 06 2002

Keywords

• nonn
• base
• mult
• look

Comments

The range of A007500 is a subset of the range of this sequence. - Reinhard Zumkeller, Jul 06 2009

Prime factors counted with multiplicity. - Harvey P. Dale, Jul 08 2017

Examples

			a(143) = a(11*13) = a(11)*a(13) = 11*31 = 341.
		

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..10000
• Index to divisibility sequences

Crossrefs

Cf. A151764, A161594, A151765. For records see A151766, A151767.

Cf. A151768 (complement), A376858 (fixed points).

Cf. A027746.

Programs

Haskell

a071786 = product . map a004086 . a027746_row
-- Reinhard Zumkeller, Oct 14 2011

Maple

read("transforms") ; A071786 := proc(n) local ifs, a, d ; ifs := ifactors(n)[2] ; a := 1 ; for d in ifs do a := a*digrev(op(1, d))^op(2, d) ; od: a ; end: # R. J. Mathar, Jun 16 2009
# second Maple program:
r:= n-> (s-> parse(cat(seq(s[-i], i=1..length(s)))))(""||n):
a:= n-> mul(r(i[1])^i[2], i=ifactors(n)[2]):
seq(a(n), n=1..100);  # Alois P. Heinz, Jun 19 2017

Mathematica

Table[Times@@IntegerReverse/@Flatten[Table[#[[1]],#[[2]]]&/@ FactorInteger[ n]],{n,80}] (* Harvey P. Dale, Jul 08 2017 *)

PARI

rev(n)=fromdigits(Vecrev(digits(n)))
a(n)=my(f=factor(n)); prod(i=1,#f~,rev(f[i,1])^f[i,2]) \\ Charles R Greathouse IV, Jun 28 2015

Python

from sympy import factorint
from operator import mul
from functools import reduce
def A071786(n):
    return 1 if n==1 else reduce(mul,(int(str(p)[::-1])**e for p,e in factorint(n).items())) # Chai Wah Wu, Aug 14 2014

Formula

Completely multiplicative with a(p) = A004086(p), p prime.

a(A000040(n)) = A004087(n).