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

Author

Jaroslav Krizek, Aug 09 2016

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

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

Programs

Magma

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

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 *)

Formula

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