OFFSET
1,13
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
G. Martin, Dimensions of the spaces of cusp forms and newforms on Gamma_0(N) and Gamma_1(N), J. Numb. Theory 112 (2005) 298-331.
FORMULA
a(n) = A029937(n) - sum a(m)*d(n/m), where the summation is over all divisors 1 < m < n of n and d is the divisor function.
EXAMPLE
a(p) = A029937(p) = (p-5)*(p-7)/24 for any prime p>3.
G.f. = x^11 + 2*x^13 + x^14 + x^15 + 2*x^16 + 5*x^17 + 2*x^18 + 7*x^19 + ...
MATHEMATICA
a[ n_] := If[ n < 1, 0, Sum[ DivisorSum[ n/j, MoebiusMu[#] MoebiusMu[n/j/#] &] If[ j < 5, 0, 1 + DivisorSum[ j, #^2 MoebiusMu[ j/#] / 24 - EulerPhi [#] EulerPhi[j/#] / 4 &]], {j, Divisors@n}]]; (* Michael Somos, May 10 2015 *)
PROG
(PARI) {a(n) = if( n<1, 0, sumdiv(n, j, sumdiv(n/j, k, moebius(k) * moebius(n/j/k)) * if( j<5, 0, 1 + sumdiv(j, k, k^2 * moebius(j/k) / 24 - eulerphi(k) * eulerphi(j/k) / 4))))}; /* Michael Somos, May 10 2015 */
CROSSREFS
KEYWORD
nonn
AUTHOR
Steven Finch, Apr 03 2009
STATUS
approved