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
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.
Programs
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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).
Comments