OFFSET
1,1
COMMENTS
Form the infinite product x*[(1-x)*(1-x^11)*(1-x^2)*(1-x^22)*(1-x^3)*(1-x^33)*(1-x^4)*(1-x^44)*...]^2 and take the coefficients of x^2, x^3, x^5, x^7, x^11, x^13, x^17, x^19, ...
The primes p where A006571(p) == 0 (mod p) are called supersingular for the elliptic curve "11a3" and are given by sequence A006962. - Michael Somos, Dec 25 2010
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000 (first 1229 terms N. J. A. Sloane)
Goro Shimura, A reciprocity law in non-solvable extensions, J. Reine Angew. Math. 221 1966 209-220.
G. Shimura, A reciprocity law in non-solvable extensions, J. Reine Angew. Math. 221 1966 209-220. [Annotated scan of pages 218, 219 only]
FORMULA
a(n) == 1 + prime(n) (mod 5) if prime(n) != 11. - Seiichi Manyama, Sep 17 2016
Conjecture: a(n) = Sum_{k=1..prime(n)} Sum_{y=1..prime(n)} Sum_{x=1..prime(n)} (A023900(k)/prime(n))[GCD(f(x,y), prime(n)) = k], where f(x,y) = x^3 - x^2 - y^2 - y. - Mats Granvik, Oct 09 2023
MATHEMATICA
a[ n_] := If[ n < 1, 0, With[ {m = Prime @ n}, SeriesCoefficient[ q (Product[ (1 - q^(11 k)), {k, Ceiling[m/11]}]Product[ 1 - q^k, {k, m}])^2, {q, 0, m}]]] (* Michael Somos, Jul 04 2011 *)
CROSSREFS
KEYWORD
sign,easy,nice
AUTHOR
N. J. A. Sloane, Sep 13 2003
STATUS
approved