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A007956 Product of proper divisors of n. 29
1, 1, 1, 2, 1, 6, 1, 8, 3, 10, 1, 144, 1, 14, 15, 64, 1, 324, 1, 400, 21, 22, 1, 13824, 5, 26, 27, 784, 1, 27000, 1, 1024, 33, 34, 35, 279936, 1, 38, 39, 64000, 1, 74088, 1, 1936, 2025, 46, 1, 5308416, 7, 2500, 51, 2704, 1, 157464, 55, 175616, 57, 58, 1, 777600000, 1, 62, 3969, 32768, 65 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = A007955(n)/n = n^(A000005(n)/2-1) = sqrt(n^(number of factors of n other than 1 and n))

a(n) = Product_{k=1..A000005(n)-1} A027751(n,k). - Reinhard Zumkeller, Feb 04 2013

a(n) = A240694(n, A000005(n)-1) for n > 1. - Reinhard Zumkeller, Apr 10 2014

MAPLE

A007956 := n -> mul(i, i=op(numtheory[divisors](n) minus {1, n}));

seq(A007956(i), i=1..79); # Peter Luschny, Mar 22 2011

MATHEMATICA

Table[Times@@Most[Divisors[n]], {n, 65}] (* Alonso del Arte, Apr 18 2011 *)

a[n_] := n^(DivisorSigma[0, n]/2 - 1); Table[a[n], {n, 1, 65}] (* Jean-Fran├žois Alcover, Oct 07 2013 *)

PROG

(PARI) A007956(n) = local(a); a=1; fordiv(n, d, a=a*d); a/n \\ Michael B. Porter, Dec 01 2009

(PARI) a(n)=my(k); if(issquare(n, &k), k^(numdiv(n)-2), n^(numdiv(n)/2-1)) \\ Charles R Greathouse IV, Oct 15 2015

(Haskell)

a007956 = product . a027751_row

-- Reinhard Zumkeller, Feb 04 2013, Nov 02 2011

CROSSREFS

Cf. A000005, A007955, A048671, A182936, A027751, A066729.

Cf. A007422 (fixed points).

Cf. A001065 (sums of proper divisors).

Sequence in context: A166120 A318256 A264859 * A107754 A181569 A274085

Adjacent sequences:  A007953 A007954 A007955 * A007957 A007958 A007959

KEYWORD

nonn,easy,nice

AUTHOR

R. Muller

EXTENSIONS

More terms from Scott Lindhurst (ScottL(AT)alumni.princeton.edu)

STATUS

approved

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Last modified November 19 00:12 EST 2018. Contains 317332 sequences. (Running on oeis4.)