OFFSET
1,1
COMMENTS
If it exists, a(6) > 10^20.
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.
EXAMPLE
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, ...
------------------------------------------------ ---- - --------------
Two successive numbers of the form p^3 * q^2 diff n a(n)
------------------------------------------------ ---- - --------------
2^3 * 3^2 = 72 | 3^3 * 2^2 = 108 36 1 72
3^3 * 7^2 = 1323 | 2^3 * 13^2 = 1352 29 2 1323
2^3 * 13^2 = 1352 | 7^3 * 2^2 = 1372 20 3 1352
3^3 * 43^2 = 49923 | 2^3 * 79^2 = 49928 5 4 49923
5^3 * 470957^2 = ... | 2^3 * 1861621^2 = ... 3 5 27725061981125
CROSSREFS
KEYWORD
nonn,fini
AUTHOR
Jon E. Schoenfield, Nov 29 2023
STATUS
approved