This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A284833 Expansion of Sum_{i>=1} x^prime(i)/(1 - x^prime(i)) * Product_{j=1..i} 1/(1 - x^prime(j)). 0
 0, 1, 1, 2, 2, 5, 3, 7, 6, 11, 8, 17, 12, 22, 21, 28, 27, 41, 35, 53, 52, 66, 66, 90, 85, 112, 114, 140, 143, 182, 180, 219, 236, 269, 291, 342, 353, 417, 444, 508, 540, 625, 657, 751, 812, 901, 974, 1097, 1168, 1313, 1414, 1562, 1684, 1874, 2008, 2219, 2397, 2626, 2832, 3121, 3341, 3668, 3956, 4305, 4650 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Total number of largest parts in all partitions of n into prime parts. LINKS FORMULA G.f.: Sum_{i>=1} x^prime(i)/(1 - x^prime(i)) * Product_{j=1..i} 1/(1 - x^prime(j)). EXAMPLE a(10) = 11 because we have [7, 3], [5, 5], [5, 3, 2], [3, 3, 2, 2], [2, 2, 2, 2, 2] and 1 + 2 + 1 + 2 + 5 = 11. MATHEMATICA nmax = 65; Rest[CoefficientList[Series[Sum[x^Prime[i]/(1 - x^Prime[i]) Product[1/(1 - x^Prime[j]), {j, 1, i}], {i, 1, nmax}], {x, 0, nmax}], x]] PROG (PARI) x='x+O('x^66); concat([0], Vec(sum(i=1, 66, x^prime(i)/(1 - x^prime(i)) * prod(j=1, i, 1/(1 - x^prime(j)))))) \\ Indranil Ghosh, Apr 04 2017 CROSSREFS Cf. A000607, A046746, A084993, A092311, A281544, A284827. Sequence in context: A286109 A239665 A178179 * A321202 A308160 A151729 Adjacent sequences:  A284830 A284831 A284832 * A284834 A284835 A284836 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Apr 03 2017 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 25 17:47 EDT 2019. Contains 324353 sequences. (Running on oeis4.)