A368490 Phi-analog of the 5-core partition function.

1, 2, 4, 8, 14, 14, 20, 24, 20, 14, 32, 24, 24, 48, 60, 32, 62, 64, 28, 40, 66, 24, 48, 88, 68, 74, 120, 80, 72, 60, 76, 64, 84, 96, 160, 96, 98, 144, 80, 48, 128, 84, 48, 168, 168, 98, 220, 184, 88, 86, 172, 64, 144, 208, 200, 168, 204, 160, 120, 120, 128, 124, 128, 168, 254, 192, 240, 264, 192, 88, 228, 144

Offset: 0

Author

Subhajit Bandyopadhyay, Dec 27 2023

Keywords

• easy
• nonn

Comments

a_t(n), the phi-analog of the t-core partition function, is defined in the article by Gireesh, Ray and Shivashankar (2021). This sequence is for a_5(n).

Links

• S. Bandyopadhyay and N. D. Baruah, Arithmetic Identities for Some Analogs of the 5-Core Partition Function, Journal of Integer Sequences, 27 (2024): Article 24.4.5.
• Subhajit Bandyopadhyay and Nayandeep Deka Baruah, Arithmetic Identities for Some Analogs of 5-core Partition Function, arXiv:2409.02034 [math.NT], 2024.
• D. S. Gireesh, C. Ray, and C. Shivashankar, A new analogue of t-core partitions, Acta Arithmetica, 199 (2021):33-53.

Crossrefs

Cf. A053723, A368495.

Programs

PARI

q='q+O('q^71);
phi(q)=eta(q^2)^5 / (eta(q)*eta(q^4))^2;
gf=phi(-q^5)^5/phi(-q);
Vec(%) \\ Joerg Arndt, Dec 27 2023

Formula

G.f.: phi(-q^5)^5/phi(-q), where phi(q) is the Ramanujan's theta function phi (see A000122).