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%I A020479 #14 Aug 03 2024 07:10:03
%S A020479 10,33,160,145,1008,385,2560,2673,7120,1441,16128,2353,26320,27585,
%T A020479 40960,5185,81648,7201,113920,97713,155056,12673,258048,90625,299728,
%U A020479 216513,421120,25201,671760,30721,655360,552321,866320,532945,1306368,51985
%N A020479 Number of noninvertible 2 X 2 matrices over Z/nZ (determinant is a divisor of 0).
%F A020479 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]
%F A020479 a(n) = n^4 - A000252(n). - _T. D. Noe_, Jan 16 2006
%t A020479 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 *)
%o A020479 (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
%Y A020479 Cf. A000252.
%K A020479 nonn
%O A020479 2,1
%A A020479 _David W. Wilson_

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