This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A109361 a(n) = Product_{k=1..n} sigma(k)/d(k), where sigma(k) = Sum_{j|k} j and d(k) = Sum_{j|k} 1. Set a(n) = 0 if the corresponding product is not an integer (e.g., for n=2 and n=10). 0
 1, 0, 3, 7, 21, 63, 252, 945, 4095, 0, 110565, 515970, 3611790, 21670740, 130024440, 806151528, 7255363752, 47159864388, 471598643880, 3301190507160, 26409524057280, 237685716515520, 2852228598186240, 21391714486396800 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The product at n = 2 is the noninteger 1.5. The product at n = 10 is the noninteger 18427.5. Jack Brennen's observed that the only values which are not integers occur when n = 2 or 10, for n < 5000. Are all products for n >= 11 integers? No other noninteger found up to 200000. - Michel Marcus, Sep 14 2015 LINKS FORMULA Product_{k=1..n} sigma(k)/d(k) = Product_{p=primes} Product_{k>=1} ((p^(k+1)-1)*k/((p^k -1)(k+1)))^floor(n/p^k). a(n) = A066780(n)/A066843(n) if this is an integer, else 0. - Michel Marcus, Sep 14 2015 EXAMPLE a(4) = 1 * 3 * 4 * 7 /(1 * 2 * 2 * 3) = 7. MATHEMATICA Table[If[IntegerQ[Product[DivisorSigma[1, k]/Length[Divisors[k]], {k, 1, n}]], Product[DivisorSigma[1, k]/Length[Divisors[k]], {k, 1, n}], 0], {n, 1, 30}] (* Stefan Steinerberger, Oct 24 2007 *) PROG (PARI) a(n) = my(q = prod(k=1, n, sigma(k)/numdiv(k))); if (denominator(q)==1, q, 0); \\ Michel Marcus, Sep 14 2015 CROSSREFS Cf. A000005, A000203. Cf. A066780, A066843. Sequence in context: A141495 A151412 A121797 * A052805 A148674 A148675 Adjacent sequences:  A109358 A109359 A109360 * A109362 A109363 A109364 KEYWORD nonn AUTHOR Leroy Quet, Aug 22 2005 EXTENSIONS More terms from Stefan Steinerberger, Oct 24 2007 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.