login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A276181 Fricke's 37 cases for two-valued modular equations. 1
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 29, 31, 32, 35, 36, 39, 41, 47, 49, 50, 59, 71 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Harvey Cohn, Fricke's Two-Valued Modular Equations, Math. Comp. 51 (1988), 787-807.
FORMULA
Numbers n>1 such that 0 = A276183(n).
PROG
(PARI)
A000003(n) = qfbclassno(-4*n);
A000089(n) = {
if (n%4 == 0 || n%4 == 3, return(0));
if (n%2 == 0, n \= 2);
my(f = factor(n), fsz = matsize(f)[1]);
prod(k = 1, fsz, if (f[k, 1] % 4 == 3, 0, 2));
};
A000086(n) = {
if (n%9 == 0 || n%3 == 2, return(0));
if (n%3 == 0, n \= 3);
my(f = factor(n), fsz = matsize(f)[1]);
prod(k = 1, fsz, if (f[k, 1] % 3 == 2, 0, 2));
};
A001615(n) = {
my(f = factor(n), fsz = matsize(f)[1],
g = prod(k=1, fsz, (f[k, 1]+1)),
h = prod(k=1, fsz, f[k, 1]));
return((n*g)\h);
};
A001616(n) = {
my(f = factor(n), fsz = matsize(f)[1]);
prod(k = 1, fsz, f[k, 1]^(f[k, 2]\2) + f[k, 1]^((f[k, 2]-1)\2));
};
A001617(n) = 1 + A001615(n)/12 - A000089(n)/4 - A000086(n)/3 - A001616(n)/2;
A276183(n) = {
my(r = if (n%8 == 3, 4, n%8 == 7, 6, 3));
if (n < 5, 0, (1 + A001617(n))/2 - r * A000003(n)/12);
};
select(x->(x>1), Vec(select(x->x==0, vector(100, n, A276183(n)), 1)))
CROSSREFS
Sequence in context: A085380 A335469 A274399 * A171829 A162421 A275164
KEYWORD
nonn,fini,full
AUTHOR
Gheorghe Coserea, Oct 17 2016
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 05:02 EDT 2024. Contains 371235 sequences. (Running on oeis4.)