A341973 Number of partitions of n into 2 distinct primes (counting 1 as a prime).

1, 1, 1, 1, 1, 2, 1, 1, 0, 2, 1, 2, 1, 2, 0, 3, 1, 3, 1, 2, 0, 4, 1, 2, 0, 2, 0, 4, 1, 3, 1, 3, 0, 4, 0, 2, 1, 3, 0, 5, 1, 4, 1, 3, 0, 6, 1, 4, 0, 3, 0, 6, 1, 3, 0, 3, 0, 7, 1, 3, 1, 5, 0, 6, 0, 3, 1, 5, 0, 7, 1, 5, 1, 5, 0, 7, 0, 5, 1, 4, 0, 9, 1, 4, 0, 4, 0, 10, 1, 4, 0, 4, 0, 7

Offset

3,6

Links

Alois P. Heinz, Table of n, a(n) for n = 3..10000

Formula

a(n) = A117929(n) + A010051(n-1). - R. J. Mathar, Oct 01 2021

Maple

b:= proc(n, i) option remember; series(`if`(n=0, 1,
     `if`(i<0, 0, (p-> `if`(p>n, 0, x*b(n-p, i-1)))(
     `if`(i=0, 1, ithprime(i)))+b(n, i-1))), x, 3)
    end:
a:= n-> coeff(b(n, numtheory[pi](n)), x, 2):
seq(a(n), n=3..96);  # Alois P. Heinz, Feb 24 2021

Mathematica

a[n_] := Select[IntegerPartitions[n, {2}, Join[{1},
    Prime[Range[PrimePi[n-1]]]]], #[[1]] != #[[2]]&] // Length;
a /@ Range[3, 100] (* Jean-François Alcover, Jul 13 2021 *)

Crossrefs

Cf. A008578, A036497, A117929, A154804, A341945, A341974, A341975, A341976, A341977.

Sequence in context: A277487 A144032 A137686 * A143792 A230121 A029375

Adjacent sequences: A341970 A341971 A341972 * A341974 A341975 A341976

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 24 2021

Status

approved