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

0,2

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

Table of n, a(n) for n=0..71.

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.

Formula

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

Prog

(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

Crossrefs

Cf. A053723, A368495.

Sequence in context: A354687 A253766 A397169 * A076380 A392347 A370840

Adjacent sequences: A368487 A368488 A368489 * A368491 A368492 A368493

Keyword

easy,nonn

Author

Subhajit Bandyopadhyay, Dec 27 2023

Status

approved