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A368490 Phi-analog of the 5-core partition function. 1
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 (list; graph; refs; listen; history; text; internal format)
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
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.
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
Sequence in context: A174540 A354687 A253766 * A076380 A370840 A049133
KEYWORD
easy,nonn
AUTHOR
STATUS
approved

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Last modified May 26 04:31 EDT 2024. Contains 372807 sequences. (Running on oeis4.)