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A275786 a(n) = Product_{d|n} T(d) where T(x) = x*(x+1)/2 = A000217(x) = x-th triangular number. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 20 23:24 EST 2019. Contains 320362 sequences. (Running on oeis4.)