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).

1, 3, 4, 7, 13, 19, 25, 31, 39, 43, 48, 91, 97, 103, 109, 117, 151, 157, 181, 193, 211, 241, 244, 247, 271, 289, 292, 301, 309, 325, 337, 349, 367, 388, 409, 421, 439, 487, 523, 547, 571, 597, 601, 613, 628, 631, 633, 687, 691, 703, 711, 733, 769, 772, 793, 811

Offset

1,2

Comments

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

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

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

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.
25 is a member as 2551 is prime.
Divisors of 39 are 1,3,13,39; reverse concatenation of divisors 391331 is prime.
48 is a member as 48241612864321 is a prime.

Maple

select(n->isprime(parse(cat("", op(sort([op(numtheory[divisors](n))], `>`))))), [$1..3000])[]; (Alec Mihailovs, Aug 14 2005)

Mathematica

Join[{1}, Select[Range[1000], PrimeQ[FromDigits[Flatten[IntegerDigits/@Reverse[Divisors[ #]]]]]&]] (* Harvey P. Dale, Feb 11 2024 *)

Crossrefs

Cf. A069582, A323427 (primes p such that p^2 is in the sequence).

Sequence in context: A088764 A093124 A055664 * A029552 A193883 A227038

Adjacent sequences: A089371 A089372 A089373 * A089375 A089376 A089377

Keyword

base,nonn

Author

Amarnath Murthy, Nov 08 2003

Extensions

Corrected and extended by David Wasserman, Sep 15 2005

Edited by N. J. A. Sloane, Apr 29 2007, Aug 14 2010

Status

approved