A275786 a(n) = Product_{d|n} T(d) where T(x) = x*(x+1)/2 = A000217(x) = x-th triangular number.

1, 3, 6, 30, 15, 378, 28, 1080, 270, 2475, 66, 294840, 91, 8820, 10800, 146880, 153, 2908710, 190, 5197500, 38808, 50094, 276, 3184272000, 4875, 95823, 102060, 35809200, 435, 17401230000, 496, 77552640, 222156, 273105, 264600, 1511016670800, 703, 422370, 425880

Offset

1,2

Comments

Conjecture: the sequence is injective (all terms of this sequence occur only once).

Links

Jaroslav Krizek, Table of n, a(n) for n = 1..1000

Formula

a(p) = A000217(p) = p*(p+1)/2 for a prime p.

Example

a(4) = 30 because the divisors of 4 are: 1, 2 and 4; and T(1)*T(2)*T(4) = 1*3*10 = 30.

Maple

f:= n -> convert(map(t -> t*(t+1)/2, numtheory:-divisors(n)), `*`):
map(f, [$1..100]); # Robert Israel, Aug 09 2016

Mathematica

t[n_]:=Divisors[n]*(Divisors[n]+1)/2; a[n_]:=Times@@t[n]; Array[a, 50] (* Ivan N. Ianakiev, Aug 15 2016 *)

Prog

(Magma) [(&*[d*(d+1) div 2: d in Divisors(n)]): n in [1..100]]

Crossrefs

Cf. A000217, A007437 (Sum_{d|n} T(d)).

Sequence in context: A007452 A046981 A065943 * A025555 A200925 A140814

Adjacent sequences: A275783 A275784 A275785 * A275787 A275788 A275789

Keyword

nonn

Author

Jaroslav Krizek, Aug 09 2016

Status

approved