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A275700 a(n) = Product_{d|n} prime(d). 9
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
a(n) mod n = 0 for n: 1, 2, 6, 30, 78, 330, 390, 870, 1410, 3198, ...
LINKS
EXAMPLE
a(4) = 42 because the divisors of 4 are: 1, 2 and 4; and prime(1) * prime(2) * prime(4) = 2 * 3 * 7 = 42.
MATHEMATICA
Table[Times@@(Prime[#]&/@Divisors[n]), {n, 50}] (* Harvey P. Dale, Jun 16 2017 *)
PROG
(Magma) [(&*[NthPrime(d): d in Divisors(n)]): n in [1..100]]
(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
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.
Sequence in context: A111414 A308486 A202533 * A258899 A248784 A341337
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Aug 05 2016
STATUS
approved

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Last modified July 18 15:51 EDT 2024. Contains 374388 sequences. (Running on oeis4.)