OFFSET
1,2
COMMENTS
Number of involutory matrices mod n. - Charles R Greathouse IV, May 29 2013
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = A066947(n) + 1.
a(n) is multiplicative and for an odd prime power p^k : a(p^k) = 2 + p^(2k-1)(p+1). [corrected by Felix A. Pahl, Mar 08 2013]
From Amiram Eldar, Nov 03 2023: (Start)
Dirichlet g.f.: ((1+1/2^s+7/2^(2*s-1)+5/2^(3*s-4))/(1+5/2^s)) * (zeta(s)*zeta(s-2)/zeta(s-1)) * Product_{p prime} (1 + 2/p^(s-1) + 1/p^s).
Sum_{k=1..n} a(k) ~ c * n^3, where c = (4*zeta(3)/13) * Product_{p prime} (1 + 1/p^2 + 1/p^3 - 2/p^4 - 1/p^5) = 0.55646002711570137209... . (End)
MATHEMATICA
f[p_, e_] := p^(2*e-1)*(p+1) + 2; f[2, e_] := 9*4^(e-1)+32; f[2, 1] = 4; f[2, 2] = 28; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Nov 02 2023 *)
PROG
(PARI) a(n)=my(o=valuation(n, 2), f=factor(n>>o)); prod(i=1, #f[, 1], f[i, 1]^(2*f[i, 2])+f[i, 1]^(2*f[i, 2]-1)+2)*if(o, if(o>1, if(o>2, 9*4^(o-1)+32, 28), 4), 1) \\ Charles R Greathouse IV, May 29 2013
CROSSREFS
KEYWORD
nonn,mult,easy
AUTHOR
Sharon Sela (sharonsela(AT)hotmail.com), Jan 26 2002
EXTENSIONS
Added more terms (from A066947), Joerg Arndt, Mar 08 2013
STATUS
approved