The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A289259 Numbers k such that k^2 divides 2^k + 3^k. 1
 1, 5, 55, 1971145, 3061355, 109715901845, 340799222665 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS If k is in the sequence and p is a prime factor, coprime to k, of 2^k + 3^k, then k*p is in the sequence. 55 = 5 * 11 1971145 = 5 * 11 * 35839 3061355 = 5 * 11 * 55661 109715901845 = 5 * 11 * 35839 * 55661 340799222665 = 5 * 11 * 55661 * 111323 See Known Terms link for additional terms. From Felix Fröhlich, Jun 29 2017: (Start) For k in the sequence, A220235(k) = 0. Subsequence of A045576. (End) LINKS Robert Israel and Ray Chandler, Known Terms A. Velampalli et al, Mathematics StackExchange, Can you prove or disprove that there exist infinitely many integers n such that n^2 divides 2^n+3^n? EXAMPLE 2^5 + 3^5 = 275 is divisible by 5^2, so 5 is in the sequence. MAPLE select(t -> 2&^t + 3&^t mod t^2 = 0, [\$1..10^6]); PROG (PARI) is(n) = Mod(2, n^2)^n==-3^n \\ Felix Fröhlich, Jun 29 2017 (PARI) is(n) = Mod(2, n^2)^n+Mod(3, n^2)^n==0 \\ Charles R Greathouse IV, Jun 29 2017 CROSSREFS Cf. A007689, A045576, A220235. Sequence in context: A129440 A045729 A067515 * A072318 A174514 A041995 Adjacent sequences:  A289256 A289257 A289258 * A289260 A289261 A289262 KEYWORD nonn,more AUTHOR Robert Israel, Jun 29 2017 EXTENSIONS a(6)-a(7) confirmed as next terms by Ray Chandler, Jul 02 2017 Known terms updated and moved to a-file by Ray Chandler, Jul 03 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 16 13:06 EDT 2021. Contains 348041 sequences. (Running on oeis4.)