login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A280126 Expansion of Product_{k>=1} (1 + x^(prime(k)^2))*(1 + x^(prime(k)^3)). 1
1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 2, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,62

COMMENTS

Number of partitions of n into distinct parts that are squares of primes (A001248) or cubes of primes (A030078).

LINKS

Table of n, a(n) for n=0..97.

Index entries for related partition-counting sequences

FORMULA

G.f.: Product_{k>=1} (1 + x^(prime(k)^2))*(1 + x^(prime(k)^3)).

EXAMPLE

a(61) = 2 because we have [49, 8, 4] and [25, 27, 9].

MATHEMATICA

nmax = 120; CoefficientList[Series[Product[(1 + x^Prime[k]^2) (1 + x^Prime[k]^3), {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A000586, A001248, A030078, A106244, A111900, A111902, A131799, A168363, A280125.

Sequence in context: A082596 A296139 A321763 * A178536 A286656 A048484

Adjacent sequences:  A280123 A280124 A280125 * A280127 A280128 A280129

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 26 2016

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 11 23:45 EDT 2020. Contains 336434 sequences. (Running on oeis4.)