OFFSET
1,1
COMMENTS
a(12) > 7*10^10, if it exists.
28279283760000, 282792837600000 and 1583639890560000 are also terms.
k! is a term for k = 3 and 7, and for no other factorial of k < 10^4.
MATHEMATICA
ff[q_, s_] := (q^(s + 1) - 1)/(q - 1); f[p_, e_] := Module[{k = e, m = 2, r, s = {}}, While[{k, r} = QuotientRemainder[k, m]; k != 0 || r != 0, If[r > 0, AppendTo[s, {p^(m - 1)!, r}]; ]; m++]; Times @@ ff @@@ s]; fsigma[1] = 1; fsigma[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[10^6], fsigma[#] == 2*# &]
PROG
(PARI) fdigits(n) = {my(k = n, m = 2, r, s = []); while([k, r] = divrem(k, m); k != 0 || r != 0, s = concat(s, r); m++); s; }
fsigma(n) = {my(f = factor(n), p = f[, 1], e = f[, 2], d); prod(i = 1, #p, prod(j = 1, #d=fdigits(e[i]), (p[i]^(j!*(d[j]+1)) - 1)/(p[i]^j! - 1))); }
is(k) = fsigma(k) == 2*k;
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Amiram Eldar, Oct 08 2024
STATUS
approved