|
| |
|
|
A002095
|
|
Number of partitions of n into nonprime parts.
(Formerly M0271 N0094)
|
|
8
| |
|
|
1, 1, 1, 1, 2, 2, 3, 3, 5, 6, 8, 8, 12, 13, 17, 19, 26, 28, 37, 40, 52, 58, 73, 79, 102, 113, 139, 154, 191, 210, 258, 284, 345, 384, 462, 509, 614, 679, 805, 893, 1060, 1171, 1382, 1528, 1792, 1988, 2319, 2560, 2986, 3304, 3823, 4231, 4888, 5399, 6219, 6870
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,5
|
|
|
COMMENTS
| Partial sums of A023895. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 19 2006
|
|
|
REFERENCES
| L. M. Chawla and S. A. Shad, On a trio-set of partition functions and their tables, J. Natural Sciences and Mathematics, 9 (1969), 87-96.
A. Murthy, Some new Smarandache sequences, functions and partitions, Smarandache Notions Journal Vol. 11 N. 1-2-3 Spring 2000 (but beware errors).
Amarnath Murthy and Charles Ashbacher, Generalized Partitions and Some New Ideas on Number Theory and Smarandache Sequences, Hexis, Phoenix; USA 2005. See Section 2.6.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n=0..1000
|
|
|
FORMULA
| G.f.: Product_{i>0} (1-x^prime(i))/(1-x^i). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 31 2004
|
|
|
EXAMPLE
| a(6) = 3 from the partitions 6=1+1+1+1+1+1=4+1+1.
|
|
|
MAPLE
| g:=product((1-x^ithprime(j))/(1-x^j), j=1..60): gser:=series(g, x=0, 60): seq(coeff(gser, x, n), n=0..55); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 19 2006
|
|
|
MATHEMATICA
| NonPrime[n_Integer] := FixedPoint[n + PrimePi[ # ] &, n + PrimePi[n]]; CoefficientList[ Series[1/Product[1 - x^NonPrime[i], {i, 1, 50}], {x, 0, 50}], x]
|
|
|
PROG
| (Haskell)
a002095 = p a018252_list where
p _ 0 = 1
p ks'@(k:ks) m = if m < k then 0 else p ks' (m - k) + p ks m
-- Reinhard Zumkeller, Jan 15 2012
|
|
|
CROSSREFS
| Cf. A000607, A018252.
Cf. A096258.
Sequence in context: A180682 A050318 A130841 * A029017 A035371 A035577
Adjacent sequences: A002092 A002093 A002094 * A002096 A002097 A002098
|
|
|
KEYWORD
| nonn,easy,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 23 1999
Corrected by Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 11 2002
|
| |
|
|
