|
Search: id:A110078
|
|
|
| A110078 |
|
a(n) is number of solutions of the equation sigma(x)=10^n. |
|
+0
3
|
|
| 1, 0, 0, 0, 2, 4, 7, 9, 15, 23, 36, 53, 85, 124, 202, 289, 425, 603, 864, 1209, 1699, 2397, 3386, 4665, 6440, 8801, 12101, 16338, 22078, 29565, 39557, 52615, 69823, 92338, 121622, 159435, 208513, 271775, 353436, 457759, 591191, 760763, 976412, 1250011
(list; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
COMMENT
|
Conjecture: For n>2, a(n+1)>a(n).
|
|
FORMULA
|
a(n) = coefficient of x^n*y^n in Prod_p Sum_{u, v} x^u*y^v, where the product is taken over all primes p and the sum is taken over such u, v that 2^u*5^v = sigma(p^k) for some nonnegative integer k. - Max Alekseyev (maxal(AT)cs.ucsd.edu), Aug 08 2005
|
|
EXAMPLE
|
a(4)=2 because 8743 & 9481 are all solutions of the equation sigma(x)=10^4.
|
|
PROGRAM
|
(PARI) { a(d) = local(X, Y, P, L, n, f, p, m, l); X=Pol([1, 0], x); Y=Pol([1, 0], y); P=Set(); L=listcreate(10000); for(i=0, d, for(j=0, d, n=2^i*5^j; if(n==1, next); f=factorint(n-1)[, 1]; for(k=1, length(f), p=f[k]; m=n*(p-1)+1; while(m%p==0, m\=p); if(m==1, l=setsearch(P, p); if(l==0, l=setsearch(P, p, 1); P=setunion(P, [p]); listinsert(L, 1, l)); L[l]+=X^i*Y^j ) ) )); R=1+O(x^(d+1))+O(y^(d+1)); for(l=1, length(L), R*=L[l]); listkill(L); vector(d+1, n, polcoeff(polcoeff(R, n-1), n-1)) } (Alekseyev)
|
|
CROSSREFS
|
Cf. A110076, A110077.
Sequence in context: A039904 A115162 A097433 this_sequence A085800 A005625 A067785
Adjacent sequences: A110075 A110076 A110077 this_sequence A110079 A110080 A110081
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Farideh Firoozbakht (f.firoozbakht(AT)math.ui.ac.ir), Aug 01 2005
|
|
EXTENSIONS
|
More terms from Max Alekseyev (maxal(AT)cs.ucsd.edu), Aug 08 2005
|
|
|
Search completed in 0.002 seconds
|
