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A341090 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.

%I A341090 #16 Feb 15 2022 21:12:56
%S A341090 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 A341090 27,28,29,30,13,32,33,142,35,36,73,38,93,40,41,42,43,44,45,46,47,48,
%U A341090 49,50,213,124,53,54,55,56,57,58,59,60,61,26,63,64,155,66
%N A341090 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 A341090 This sequence is a self-inverse permutation of the natural numbers.
%H A341090 Rémy Sigrist, <a href="/A341090/a341090.png">Scatterplot of (n, a(n)) for n, a(n) <= 1000000</a>
%H A341090 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A341090 For n = 377:
%e A341090 - 377 = 13 * 29,
%e A341090 - the reversal of 13, 31, is prime,
%e A341090 - the reversal of 29, 92, is not prime,
%e A341090 - so a(377) = 31 * 29 = 899.
%p A341090 R:= n-> (s-> parse(cat(s[-i]$i=1..length(s))))(""||n):
%p A341090 a:= proc(n) option remember; mul((q->
%p A341090      `if`(isprime(q), q, j[1]))(R(j[1]))^j[2], j=ifactors(n)[2])
%p A341090     end:
%p A341090 seq(a(n), n=1..66);  # _Alois P. Heinz_, Feb 15 2022
%t A341090 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 A341090 (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 A341090 Cf. A004086, A071786, A235027.
%K A341090 nonn,base,mult
%O A341090 1,2
%A A341090 _Rémy Sigrist_, Feb 13 2022