OFFSET
0,5
COMMENTS
Conjecture: For n>2, a(n+1)>a(n).
LINKS
Max Alekseyev, Table of n, a(n) for n = 0..1000
Max A. Alekseyev, Computing the Inverses, their Power Sums, and Extrema for Euler's Totient and Other Multiplicative Functions. Journal of Integer Sequences, Vol. 19 (2016), Article 16.5.2
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, Aug 08 2005
EXAMPLE
a(4)=2 because 8743 & 9481 are all solutions of the equation sigma(x)=10^4.
PROG
(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
KEYWORD
nonn
AUTHOR
Farideh Firoozbakht, Aug 01 2005
EXTENSIONS
More terms from Max Alekseyev, Aug 08 2005
Terms a(44) onward from Max Alekseyev, Mar 04 2014
STATUS
approved