OFFSET
1,2
COMMENTS
Positions of records in {f(k) | k = 1, 2, ...}, where f(k) = (Sum_{d|k} sigma(d)/d) / tau(k) = A374777(k)/A374778(k), i.e., numbers k such that f(k) > f(m) for all m < k.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..778
EXAMPLE
MATHEMATICA
f[p_, e_] := ((e+1)*p^2 - (e+2)*p + p^(-e))/((e+1)*(p-1)^2); s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; seq[kmax_] := Module[{v = {}, smax = 0, s1}, Do[s1 = s[k]; If[s1 > smax, AppendTo[v, k]; smax = s1], {k, 1, kmax}]; v]; seq[10^5]
PROG
(PARI) s(n) = {my(f = factor(n)); prod(i = 1, #f~, p=f[i, 1]; e=f[i, 2]; (-2*p - e*p + p^2 + e*p^2 + p^(-e))/((e + 1)*(p - 1)^2)); }
lista(kmax) = {my(smax = 0, s1); for(k = 1, kmax, s1 = s(k); if(s1 > smax, print1(k, ", "); smax = s1)); }
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jul 19 2024
STATUS
approved