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A089374 Numbers n such that the concatenation (in descending order) of all the divisors of n, with 1 in the least significant position, is prime (or 1).

%I A089374 #19 Feb 11 2024 14:32:16
%S A089374 1,3,4,7,13,19,25,31,39,43,48,91,97,103,109,117,151,157,181,193,211,
%T A089374 241,244,247,271,289,292,301,309,325,337,349,367,388,409,421,439,487,
%U A089374 523,547,571,597,601,613,628,631,633,687,691,703,711,733,769,772,793,811
%N A089374 Numbers n such that the concatenation (in descending order) of all the divisors of n, with 1 in the least significant position, is prime (or 1).
%C A089374 See A176558(n) = reverse concatenation of divisors of n. See A175355 for corresponding values of reverse concatenations. Complement of A175354(n) for n >= 2. - _Jaroslav Krizek_, Apr 20 2010
%C A089374 If prime p divides n, then the exponent of p in the prime factorization of n is odd if p == 1 (mod 3) and even if p == 2 (mod 3).  In particular, the sequence has no terms == 2 (mod 3). - _Robert Israel_, Apr 21 2020
%H A089374 Robert Israel, <a href="/A089374/b089374.txt">Table of n, a(n) for n = 1..10000</a>
%e A089374 4 is a term as 421 is prime; 39 is a term as concatenation of 39,13,3 and 1, i.e. 391331, is prime.
%e A089374 25 is a member as 2551 is prime.
%e A089374 Divisors of 39 are 1,3,13,39; reverse concatenation of divisors 391331 is prime.
%e A089374 48 is a member as 48241612864321 is a prime.
%p A089374 select(n->isprime(parse(cat("",op(sort([op(numtheory[divisors](n))],`>`))))),[$1..3000])[]; (Alec Mihailovs, Aug 14 2005)
%t A089374 Join[{1},Select[Range[1000],PrimeQ[FromDigits[Flatten[IntegerDigits/@Reverse[Divisors[ #]]]]]&]] (* _Harvey P. Dale_, Feb 11 2024 *)
%Y A089374 Cf. A069582, A323427 (primes p such that p^2 is in the sequence).
%K A089374 base,nonn
%O A089374 1,2
%A A089374 _Amarnath Murthy_, Nov 08 2003
%E A089374 Corrected and extended by _David Wasserman_, Sep 15 2005
%E A089374 Edited by _N. J. A. Sloane_, Apr 29 2007, Aug 14 2010