A275700 a(n) = Product_{d|n} prime(d).

2, 6, 10, 42, 22, 390, 34, 798, 230, 1914, 62, 101010, 82, 4386, 5170, 42294, 118, 547170, 134, 951258, 12410, 14694, 166, 170807910, 2134, 24846, 23690, 3285114, 218, 660741510, 254, 5540514, 42470, 49206, 55726, 21399271530, 314, 65526, 68470, 3126785046, 358

Offset: 1

Author

Jaroslav Krizek, Aug 05 2016

Keywords

• nonn

Comments

a(n) mod n = 0 for n: 1, 2, 6, 30, 78, 330, 390, 870, 1410, 3198, ...

Examples

			a(4) = 42 because the divisors of 4 are: 1, 2 and 4; and prime(1) * prime(2) * prime(4) = 2 * 3 * 7 = 42.
		

Crossrefs

Cf. A007445 (Sum_{d|n} prime(d)).

A version for binary indices is A034729.

Partitions of this type are counted by A054973, strict case of A371284.

The sorted version is A371283, squarefree case of A371288.

These numbers have products A371286, unsorted version A371285.

A000005 counts divisors, row-lengths of A027750.

A027746 lists prime factors, indices A112798, length A001222.

Cf. A000720, A001221, A005179, A007416.

Programs

Magma

[(&*[NthPrime(d): d in Divisors(n)]): n in [1..100]]

Mathematica

Table[Times@@(Prime[#]&/@Divisors[n]),{n,50}] (* Harvey P. Dale, Jun 16 2017 *)

PARI

a(n) = my(d=divisors(n)); prod(i=1, #d, prime(d[i])) \\ Felix Fröhlich, Aug 05 2016

Perl

use ntheory ":all"; sub a275700 { vecprod(map { nth_prime($) } divisors($[0])); } # Dana Jacobsen, Aug 09 2016