This site is supported by donations to The OEIS Foundation.

"Email this user" was broken Aug 14 to 9am Aug 16. If you sent someone a message in this period, please send it again.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A194260 A194259(n) - n, where A194259(n) is the number of distinct prime factors of p(1)*p(2)*...*p(n) and p(n) is the n-th partition number. 5
 -1, -1, -1, -1, -1, -1, -2, -3, -4, -5, -6, -7, -7, -8, -9, -10, -11, -12, -13, -13, -14, -14, -14, -15, -15, -15, -15, -15, -15, -15, -15, -15, -16, -16, -16, -16, -16, -17, -18, -18, -18, -18, -18, -17, -17, -16, -16, -16, -16, -16, -16, -16, -16, -15, -15, -14, -14, -14, -14, -13, -13, -13, -12, -12, -12, -12, -11, -11, -10, -10, -10, -10, -9, -9, -9, -9, -9, -8, -7, -7, -7, -8, -8, -8, -8, -7, -7, -7, -7, -6, -5, -4, -4, -4, -3, -3, -4, -4, -4, -4, -4, -3, -3, -3, -3, -3, -3, -3, -3, -2, -2, -2, -2, -2, 0, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 COMMENTS Schinzel and Wirsing proved that a(n) > C*log n - n, for any positive constant C < 1/log 2 and all large n. In fact, it appears that a(n) > 0 for all n > 115. It also appears that a(n) >= a(n-1), for all n > 97, so that some prime factor of p(n) does not divide p(1)*p(2)*...*p(n-1). LINKS Alois P. Heinz and Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 2000 terms from Alois P. Heinz) A. Schinzel and E. Wirsing, Multiplicative properties of the partition function, Proc. Indian Acad. Sci., Math. Sci. (Ramanujan Birth Centenary Volume), 97 (1987), 297-303. FORMULA a(n) = A001221(product(k=1..n, A000041(k))) - n. EXAMPLE p(1)*p(2)*...*p(8) = 1*2*3*5*7*11*15*22 = 2^2 * 3^2 * 5^2 * 7 * 11^2, so a(8) = 5 - 8 = -3. MAPLE with(combinat): with(numtheory): b:= proc(n) option remember;       `if`(n=1, {}, b(n-1) union factorset(numbpart(n)))     end: a:= n-> nops(b(n)) -n: seq(a(n), n=1..116); # Alois P. Heinz, Aug 20 2011 MATHEMATICA a[n_] := PrimeNu[Product[PartitionsP[k], {k, 1, n}]] - n; Table[a[n], {n, 1, 116}] (* Jean-François Alcover, Jan 28 2014 *) CROSSREFS Cf. A000041, A001221, A087175, A194259. Sequence in context: A101041 A093697 A157466 * A227394 A209900 A097043 Adjacent sequences:  A194257 A194258 A194259 * A194261 A194262 A194263 KEYWORD sign AUTHOR Jonathan Sondow, Aug 20 2011 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.