cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A280126 Expansion of Product_{k>=1} (1 + x^(prime(k)^2))*(1 + x^(prime(k)^3)).

Original entry on oeis.org

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
Offset: 0

Views

Author

Ilya Gutkovskiy, Dec 26 2016

Keywords

Comments

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

Examples

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

Links

Crossrefs

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

Programs

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

Formula

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

A280715 Expansion of Product_{k>=1} 1/((1 - x^prime(k))*(1 - x^(prime(k)^2))*(1 - x^(prime(k)^3))).

Original entry on oeis.org

1, 0, 1, 1, 2, 2, 3, 4, 6, 7, 9, 12, 15, 19, 23, 29, 36, 44, 53, 65, 78, 94, 112, 134, 159, 189, 222, 263, 307, 361, 420, 491, 569, 661, 764, 883, 1017, 1170, 1343, 1539, 1761, 2011, 2293, 2611, 2968, 3369, 3819, 4323, 4887, 5518, 6222, 7007, 7883, 8857, 9942, 11144, 12483, 13964, 15609, 17426, 19440, 21664
Offset: 0

Views

Author

Ilya Gutkovskiy, Jan 07 2017

Keywords

Comments

Number of partitions of n into parts that are primes (A000040), squares of primes (A001248) or cubes of primes (A030078).

Examples

			a(8) = 6 because we have [8], [5, 3], [4, 4], [4, 2, 2], [3, 3, 2], [2, 2, 2, 2].

Links

Crossrefs

Cf. A000040, A000607, A001248, A023893, A030078, A087797, A090677, A111901, A279760, A280125.

Programs

  • Mathematica
    nmax = 61; CoefficientList[Series[Product[1/((1 - x^Prime[k]) (1 - x^Prime[k]^2) (1 - x^Prime[k]^3)), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Product_{k>=1} 1/((1 - x^prime(k))*(1 - x^(prime(k)^2))*(1 - x^(prime(k)^3))).
Showing 1-2 of 2 results.

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