OFFSET
1,1
COMMENTS
The numbers of terms not exceeding 10^k, for k = 2, 3, ..., are 3, 43, 399, 4292, 41306, 413310, 4155925, 414963651, 4149603572, ...
Apparently, the asymptotic density of this sequence is 0.04149...
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
44 is a term since sigma(44)/44 = 84/44 = 1.909... and sigma(45)/45 = 78/45 = 1.733... are both larger than Pi^2/6 = 1.644... .
MATHEMATICA
q[n_] := DivisorSigma[-1, n] > Pi^2/6; Select[Range[1300], q[#] && q[# + 1] &]
PROG
(PARI) isok(k) = ((sigma(k)/k) > Pi^2/6) && ((sigma(k+1)/(k+1)) > Pi^2/6); \\ Michel Marcus, Apr 25 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Apr 25 2022
STATUS
approved