login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A184172 Number of partitions of n into an odd number of distinct primes. 5
0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 2, 2, 3, 3, 3, 4, 3, 5, 3, 4, 4, 5, 5, 6, 6, 7, 5, 7, 7, 8, 8, 8, 9, 11, 9, 10, 11, 12, 12, 14, 13, 16, 14, 16, 15, 19, 17, 20, 20, 22, 20, 23, 24, 27, 26, 28, 27, 33, 30, 34, 34, 37, 36, 41, 40, 46, 43, 47, 46, 55, 50, 56 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,19

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..2000

FORMULA

G.f.: (1/2)*[Product_{k>=1} (1+z^prime(k)) - Product_{k>=1} (1-z^prime(k))].

a(n) = Sum_{k>=0} A219180(n,2*k+1). - Alois P. Heinz, Nov 15 2012

EXAMPLE

a(33) = 4 because we have [23,7,3], [19,11,3], [17,13,3], and [17,11,5].

MAPLE

g := 1/2*(Product(1+z^ithprime(k), k = 1 .. 120)-Product(1-z^ithprime(k), k = 1 .. 120)): gser := series(g, z = 0, 110): seq(coeff(gser, z, n), n = 0 .. 85);

# second Maple program

with(numtheory):

b:= proc(n, i) option remember;

      `if`(n=0, [1], `if`(i<1, [], zip((x, y)->x+y, b(n, i-1),

       [0, `if`(ithprime(i)>n, [], b(n-ithprime(i), i-1))[]], 0)))

    end:

a:= proc(n) local l; l:= b(n, pi(n));

      add(l[2*i], i=1..iquo(nops(l), 2))

    end:

seq(a(n), n=0..100);  # Alois P. Heinz, Nov 15 2012

MATHEMATICA

b[n_, i_] := b[n, i] = If[n == 0, {1}, If[i<1, {}, Plus @@ PadRight[{b[n, i-1], Join[{0}, If[Prime[i]>n, {}, b[n-Prime[i], i-1]]]}]]]; a[n_] := Module[{l}, l = b[n, PrimePi[n]]; Sum[l[[2*i]], {i, 1, Quotient[Length[l], 2]}]]; Table[a[n], {n, 0, 100}] (* Jean-Fran├žois Alcover, Jan 30 2014, after Alois P. Heinz *)

CROSSREFS

Cf. A000586, A184171.

Sequence in context: A078178 A105068 A120676 * A125973 A227196 A189172

Adjacent sequences:  A184169 A184170 A184171 * A184173 A184174 A184175

KEYWORD

nonn

AUTHOR

Emeric Deutsch (suggested by R. J. Mathar), Jan 09 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.

License Agreements, Terms of Use, Privacy Policy .

Last modified June 24 07:19 EDT 2017. Contains 288697 sequences.