This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A367781 #8 Nov 30 2023 09:47:14 %S A367781 72,1323,1352,49923,27725061981125 %N A367781 Numbers with prime signature p^3 * q^2 whose difference from the next such number is a record low. %C A367781 If it exists, a(6) > 10^20. %C A367781 Do there exist two numbers with prime signature p^3 * q^2 that differ by less than 3? If not, this sequence terminates at a(5) = 27725061981125. %e A367781 A143610, the sequence of numbers with prime signature p^3 * q^2, is 72, 108, 200, 392, 500, 675, 968, 1125, 1323, 1352, 1372, 2312, ...; the differences between its successive terms are 36, 92, 192, 108, 175, 293, 157, 198, 29, 20, 940, ..., and the first five record lows among those differences are 36, 29, 20, 5, 3, ... %e A367781 ------------------------------------------------ ---- - -------------- %e A367781 Two successive numbers of the form p^3 * q^2 diff n a(n) %e A367781 ------------------------------------------------ ---- - -------------- %e A367781 2^3 * 3^2 = 72 | 3^3 * 2^2 = 108 36 1 72 %e A367781 3^3 * 7^2 = 1323 | 2^3 * 13^2 = 1352 29 2 1323 %e A367781 2^3 * 13^2 = 1352 | 7^3 * 2^2 = 1372 20 3 1352 %e A367781 3^3 * 43^2 = 49923 | 2^3 * 79^2 = 49928 5 4 49923 %e A367781 5^3 * 470957^2 = ... | 2^3 * 1861621^2 = ... 3 5 27725061981125 %Y A367781 Cf. A143610. %K A367781 nonn,fini %O A367781 1,1 %A A367781 _Jon E. Schoenfield_, Nov 29 2023