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A020479
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Number of noninvertible 2 X 2 matrices over Z/nZ (determinant is a divisor of 0).
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1
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10, 33, 160, 145, 1008, 385, 2560, 2673, 7120, 1441, 16128, 2353, 26320, 27585, 40960, 5185, 81648, 7201, 113920, 97713, 155056, 12673, 258048, 90625, 299728, 216513, 421120, 25201, 671760, 30721, 655360, 552321, 866320, 532945, 1306368, 51985
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OFFSET
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2,1
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LINKS
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FORMULA
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a(n) seems to be divisible by n. - Ralf Stephan, Sep 01 2003 [This is true and can be easily proven from the formula below and from the multiplicative formula for A000252(n). - Amiram Eldar, Aug 03 2024]
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MATHEMATICA
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f[p_, e_] := (p - 1)^2*(p + 1)*p^(4*e - 3); a[n_] := n^4 - Times @@ f @@@ FactorInteger[n]; Array[a, 36, 2] (* Amiram Eldar, Aug 03 2024 *)
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PROG
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(PARI) a(n) = {my(f = factor(n), p = f[, 1], e=f[, 2]); n^4 - prod(k = 1, #p, (p[k] - 1)^2*(p[k] + 1)*p[k]^(4*e[k] - 3)); } \\ Amiram Eldar, Aug 03 2024
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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