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A206032
a(n) = Product_{d|n} sigma(d) where sigma = A000203.
15
1, 3, 4, 21, 6, 144, 8, 315, 52, 324, 12, 28224, 14, 576, 576, 9765, 18, 73008, 20, 95256, 1024, 1296, 24, 25401600, 186, 1764, 2080, 225792, 30, 26873856, 32, 615195, 2304, 2916, 2304, 1302170688, 38, 3600, 3136, 128595600, 42, 84934656, 44, 762048, 584064
OFFSET
1,2
COMMENTS
Sequence is not the same as A206031(n): a(66) = 429981696, A206031(66) = 35831808.
In sequence a(n) are multiplied all values of sigma(d) of all divisors d of numbers n, in sequence A206031 are multiplied only distinct values of sigma(d) of all divisors d of numbers n.
LINKS
FORMULA
a(p) = p+1, a(pq) = ((p+1)*(q+1))^2 for p, q = distinct primes.
EXAMPLE
For n=6 -> divisors d of 6: 1,2,3,6; corresponding values k of sigma(d): 1,3,4,12; a(6) = Product of k = 1*3*4*12 = 144. For n=66 -> divisors d of 66: 1,2,3,6,11,22,33,66; corresponding values k of sigma(d): 1,3,4,12,12,36,48,144; a(66) = Product of k = 1*3*4*12*12*36*48*144 = 429981696.
MATHEMATICA
Table[Times @@ DivisorSigma[1, Divisors[n]], {n, 100}] (* T. D. Noe, Feb 10 2012 *)
PROG
(PARI) a(n)=my(d=divisors(n)); prod(i=2, #d, sigma(d[i])) \\ Charles R Greathouse IV, Feb 19 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Feb 03 2012
STATUS
approved