verify.sf

#!/usr/bin/ruby

# Positions of records in A306440.
# https://oeis.org/A307221

# Where A306440(n) is defined as:
#   Number of different ways of expressing 2*n as (p - 1)*(q - 1), where p < q are primes

var h = Hash(
  "58"  => 151351200,
  "59"  => 518918400,
  "60"  => 441080640,
  "61"  => 475009920,
  "62"  => 474692400,
  "63"  => 454053600,
  "64"  => 275675400,
  "65"  => 537213600,
  "66"  => 1300622400,
  "67"  => 882161280,
  "68"  => 918918000,
  "69"  => 1232431200,
  "70"  => 735134400,
  "71"  => 1102701600,
  "72"  => 2259457200,
  "73"  => 821620800,
  "74"  => 2035756800,
  "75"  => 1187524800,
  "76"  => 1403438400,
  "77"  => 1881079200,
  "78"  => 3223281600,
  "79"  => 2095133040,
  "80"  => 2536213680,
  "81"  => 2875672800,
  "82"  => 3859455600,
  "83"  => 2205403200,
  "84"  => 2907122400,
  "85"  => 3760495200,
  "86"  => 4227022800,
  "87"  => 2940537600,
  "88"  => 6054048000,
  "89"  => 2572970400,
  "90"  => 6265939680,
  "91"  => 7764316560,
  "92"  => 6064858800,
  "93"  => 5329724400,
  "94"  => 5145940800,
  "95"  => 4929724800,
  "98"  => 5513508000,
  "100" => 7718911200,
  "102" => 7351344000,
  "103" => 8821612800,
  "104" => 9777287520,
  "107" => 6446563200,
  "110" => 8627018400,
)

# Extra terms after a(33):
#   275675400, 537213600, 735134400, 821620800, 1187524800, 1403438400, 1881079200

say h.keys.grep{Num(_)>77}.map{h{_}}.min