A244285 - OEIS

A244285

Decimal expansion of A1*B1, the average number of non-isomorphic semisimple rings of any order, where A1 is Product_{m>1} zeta(m) and B1 is Product_{r*m^2 > 1} zeta(r*m^2).

2, 4, 9, 9, 6, 1, 6, 1, 1, 2, 9, 3, 6, 2, 9, 8, 2, 7, 4, 9, 3, 2, 3, 7, 3, 8, 2, 1, 7, 5, 6, 4, 9, 8, 0, 3, 4, 5, 7, 0, 4, 0, 2, 2, 5, 8, 8, 0, 7, 5, 9, 5, 4, 4, 3, 2, 0, 6, 2, 1, 0, 9, 4, 8, 1, 2, 1, 2, 2, 4, 3, 6, 8, 1, 6, 9, 6, 5, 1, 3, 6, 4, 7, 2, 6, 8, 8, 6, 3, 3, 6, 4, 3, 0, 9, 7, 5, 3, 6, 2, 8, 7, 2, 2, 6

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OFFSET

1,1

COMMENTS

The asymptotic mean of A038538. - Amiram Eldar, Jan 31 2024

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.1 Abelian group enumeration constants, pp. 274-276.

LINKS

Table of n, a(n) for n=1..105.

EXAMPLE

2.499616112936298274932373821756498034570402258807595443206210948121224368...

MAPLE

Digits := 200: z:=product(Zeta(1.0*j), j = 2..1000): for k from 10 by 10 to 50 do print(z*product(product(Zeta(1.0*r*m^2), r = 1..k^2), m = 2..k)); end do; # Vaclav Kotesovec, Jun 11 2020

MATHEMATICA

digits = 20; digitsPlus = 100; n0 = 50; dn = 1; A1 = NProduct[Zeta[m], {m, 2, Infinity}, WorkingPrecision -> digitsPlus]; Clear[B1]; B1[n_] := B1[n] = NProduct[Zeta[r*m^2], {r, 1, n}, {m, 2, n}, WorkingPrecision -> digitsPlus]; B1[n0]; B1[n = n0 + dn]; While[ RealDigits[B1[n], 10, digitsPlus] != RealDigits[B1[n - dn], 10, digitsPlus], Print["n = ", n]; n = n + dn]; RealDigits[A1*B1[n], 10, digits] // First

PROG

(PARI) prodinf(m = 2, zeta(m)) * prodinf(r = 1, prodinf(m = 2, zeta(r*m^2))) \\ Amiram Eldar, Jan 31 2024

CROSSREFS

Cf. A021002 (A1), A038538, A123030.

Sequence in context: A163299 A337911 A198679 * A111422 A279035 A076661

Adjacent sequences: A244282 A244283 A244284 * A244286 A244287 A244288

KEYWORD

nonn,cons

AUTHOR

Jean-François Alcover, Jun 25 2014

EXTENSIONS

More digits from Vaclav Kotesovec, Jun 11 2020

STATUS

approved