A280307 Numbers m such that 7^m - 6^m is not squarefree, but 7^d - 6^d is squarefree for every proper divisor d of m.

20, 26, 55, 68, 171, 258, 310

Offset: 1

Author

Juri-Stepan Gerasimov, Dec 31 2016

Keywords

• nonn
• more

Comments

Numbers m such that 7^m - 6^m is not squarefree not divisible by any smaller number of the same form.

7^m - 6^m is nonsquarefree if and only if m is divisible by a term of this sequence. - Jon E. Schoenfield, Jan 01 2017

The smallest squares of 7^m - 6^m as defined above are 25, 169, 121, 289, 361, 1849, 961. - Robert Price, Mar 07 2017

a(8) >= 323. - Jinyuan Wang, May 15 2020

a(8) <= 381. 381, 406, 506, 610, 689, 979, 1027, 1081, 1332 are terms. - Chai Wah Wu, Jul 20 2020

Examples

			20 is in this sequence because 7^20 - 6^20 = 43242508113549025 is not squarefree but 7^d - 6^d is squarefree for every proper divisor d of 20 (i.e., for d = 1, 2, 4, 5, and 10): 7^1 - 6^1 = 1, 7^2 - 6^2 = 13, 7^4 - 6^4 = 1105, 7^5 - 6^5 = 13682, 7^10 - 6^10 = 222009013 are all squarefree.
		

Crossrefs

Cf. A016169, A237043, A280203, A280208, A280209, A280302.

Extensions

a(5)-a(7) from Jinyuan Wang, May 15 2020