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%I #16 Feb 15 2022 21:12:56
%S 1,2,3,4,5,6,7,8,9,10,11,12,31,14,15,16,71,18,19,20,21,22,23,24,25,62,
%T 27,28,29,30,13,32,33,142,35,36,73,38,93,40,41,42,43,44,45,46,47,48,
%U 49,50,213,124,53,54,55,56,57,58,59,60,61,26,63,64,155,66
%N Fully multiplicative: for any prime p, if the reversal of p in base 10, say q, is prime, then a(p) = q, otherwise a(p) = p.
%C This sequence is a self-inverse permutation of the natural numbers.
%H Rémy Sigrist, <a href="/A341090/a341090.png">Scatterplot of (n, a(n)) for n, a(n) <= 1000000</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e For n = 377:
%e - 377 = 13 * 29,
%e - the reversal of 13, 31, is prime,
%e - the reversal of 29, 92, is not prime,
%e - so a(377) = 31 * 29 = 899.
%p R:= n-> (s-> parse(cat(s[-i]$i=1..length(s))))(""||n):
%p a:= proc(n) option remember; mul((q->
%p `if`(isprime(q), q, j[1]))(R(j[1]))^j[2], j=ifactors(n)[2])
%p end:
%p seq(a(n), n=1..66); # _Alois P. Heinz_, Feb 15 2022
%t f[p_, e_] := If[PrimeQ[(q = IntegerReverse[p])], q, p]^e; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Feb 15 2022 *)
%o (PARI) a(n) = { my (f=factor(n)); prod (k=1, #f~, my (p=f[k,1], e=f[k,2], q=fromdigits(Vecrev(digits(p)))); if (isprime(q), q, p)^e) }
%Y Cf. A004086, A071786, A235027.
%K nonn,base,mult
%O 1,2
%A _Rémy Sigrist_, Feb 13 2022
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