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

1,2

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

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..10000

Index to divisibility sequences

Formula

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

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

Example

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

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 *)

Prog

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

Crossrefs

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

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

Cf. A027746.

Sequence in context: A277650 A377913 A341090 * A151766 A004852 A342046

Adjacent sequences: A071783 A071784 A071785 * A071787 A071788 A071789

Keyword

nonn,base,mult,look

Author

Reinhard Zumkeller, Jun 06 2002

Status

approved