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A038538
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Number of semisimple rings with n elements.
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8
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1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 2, 1, 1, 1, 6, 1, 2, 1, 2, 1, 1, 1, 3, 2, 1, 3, 2, 1, 1, 1, 8, 1, 1, 1, 4, 1, 1, 1, 3, 1, 1, 1, 2, 2, 1, 1, 6, 2, 2, 1, 2, 1, 3, 1, 3, 1, 1, 1, 2, 1, 1, 2, 13, 1, 1, 1, 2, 1, 1, 1, 6, 1, 1, 2, 2, 1, 1, 1, 6, 6, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 2, 1, 1, 1, 8, 1, 2, 2
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OFFSET
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1,4
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COMMENTS
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Enumeration uses Wedderburn-Artin theorem and fact that a finite division ring is a field.
a(n) depends only on prime signature of n (cf. A025487). So a(24) = a(375) since 24 = 2^3 * 3 and 375 = 3 * 5^3 both have prime signature (3,1).
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REFERENCES
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T. Y. Lam, A First Course in Noncommutative Rings, Springer-Verlag.
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 1..16384
Index entries for sequences computed from exponents in factorization of n
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FORMULA
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a(p^k) = A004101(k).
For all n, a(A002110(n)) = a(A005117(n)) = 1.
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PROG
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(PARI)
v004101from1 = [1, 2, 3, 6, 8, 13, 18, 29, 40, 58, 79, 115, 154, 213, 284, 391, 514, 690, 900, 1197]; \\ From the data-section of A004101.
A004101(n) = v004101from1[n];
vecproduct(v) = { my(m=1); for(i=1, #v, m *= v[i]); m; };
A038538(n) = vecproduct(apply(e -> A004101(e), factorint(n)[, 2])); \\ Antti Karttunen, Nov 18 2017
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CROSSREFS
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Cf. A002110, A004101, A005117, A027623, A052305.
Sequence in context: A319786 A321271 A305193 * A293515 A326622 A292777
Adjacent sequences: A038535 A038536 A038537 * A038539 A038540 A038541
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KEYWORD
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nonn,nice,mult
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AUTHOR
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Paolo Dominici (pl.dm(AT)libero.it)
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STATUS
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approved
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