A275001 Expansion of 1/(1 - Sum_{k>=1} x^(prime(k)^2)).

1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 2, 0, 0, 1, 3, 1, 0, 1, 4, 3, 0, 1, 6, 6, 1, 1, 8, 10, 4, 1, 10, 17, 10, 2, 12, 27, 20, 6, 14, 40, 38, 16, 17, 56, 68, 36, 25, 76, 114, 75, 43, 101, 180, 147, 81, 137, 273, 271, 159, 194, 401, 471, 313, 292, 579, 782, 601, 472, 832, 1251, 1109, 816

Offset

0,14

Comments

Number of compositions (ordered partitions) of n into squares of primes (A001248).

From Ilya Gutkovskiy, Feb 12 2017: (Start)

Conjecture(1): every number > 23 is the sum of at most 8 squares of primes.

Conjecture(2): every number > 131 can be represented as a sum of 13 squares of primes. (End)

Links

Table of n, a(n) for n=0..74.

Index entries for sequences related to compositions

Index entries for sequences related to sums of squares

Formula

G.f.: 1/(1 - Sum_{k>=1} x^(prime(k)^2)).

Example

a(17) = 3 because we have [4, 4, 9], [4, 9, 4] and [9, 4, 4].

Mathematica

nmax = 85; CoefficientList[Series[1/(1 - Sum[x^Prime[k]^2, {k, 1, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A001248, A006456, A023360, A090677.

Sequence in context: A045847 A137586 A291170 * A290975 A367145 A291678

Adjacent sequences: A274998 A274999 A275000 * A275002 A275003 A275004

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 24 2016

Status

approved