

A349988


a(n) is the smallest k such that n^k + (n+1)^k is divisible by a square > 1.


2



3, 5, 2, 1, 11, 10, 3, 10, 19, 3, 10, 1, 1, 29, 26, 3, 5, 3, 3, 2, 2, 1, 10, 1, 3, 10, 5, 2, 9, 3, 1, 5, 10, 3, 39, 10, 1, 7, 21, 1, 5, 5, 3, 21, 7, 2, 5, 10, 1, 78, 10, 3, 2, 26, 3, 10, 5, 1, 7, 1, 3, 1, 10, 3, 21, 7, 1, 3, 68, 3, 2, 5, 1, 21, 26, 1, 5, 2, 3
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OFFSET

1,1


COMMENTS



LINKS



FORMULA

a(9m5) = 1 for m >= 1 since a(9m5) = (9m5)^1 + (9m5+1)^1 = 18m9 which is divisible by 9 = 3^2.  Kevin P. Thompson, Jan 13 2022


EXAMPLE

a(2) = 5 since the values of 2^k + (2+1)^k for k=1..4 are 5, 13, 35, and 97, none of which are divisible by a square > 1, and 2^5 + (2+1)^5 = 275 which is divisible by 25 = 5^2.


MATHEMATICA



PROG

(PARI) a(n) = my(k=1); while(issquarefree(n^k + (n+1)^k), k++); k; \\ Michel Marcus, Dec 08 2021


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



