OFFSET
1,2
COMMENTS
The number of terms not exceeding 10^k for k = 1, 2, ... is 4, 55, 640, 6990, 74405, 778569, 8050432, 82589241, 842606359, 8562275783, ... Apparently, this sequence has an asymptotic density ~0.85.
Includes all the primes p such that (p+1)/2 is an odd prime, i.e., A005383 without the first term 3.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
5 is a term since usigma(5)/ud(5) = 6/2 = 3 is an integer, and so is usigma(3)/ud(3) = 4/2 = 2.
MATHEMATICA
usigma[1] = 1; usigma[n_] := Times @@ (1 + Power @@@ FactorInteger[n]); ud[n_] := 2^PrimeNu[n]; rat[n_] := usigma[n]/ud[n]; Select[Range[200], IntegerQ[(r = rat[#])] && IntegerQ[rat[r]] &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 12 2020
STATUS
approved