A367781 Numbers with prime signature p^3 * q^2 whose difference from the next such number is a record low.

72, 1323, 1352, 49923, 27725061981125

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.

Links

Table of n, a(n) for n=1..5.

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

Cf. A143610.

Sequence in context: A200556 A239423 A128800 * A008391 A292881 A282018

Adjacent sequences: A367778 A367779 A367780 * A367782 A367783 A367784

Keyword

nonn,fini

Author

Jon E. Schoenfield, Nov 29 2023

Status

approved