A165972 Nonprimes k such that the sum of the smallest and largest divisor of k is prime.

1, 4, 6, 10, 12, 16, 18, 22, 28, 30, 36, 40, 42, 46, 52, 58, 60, 66, 70, 72, 78, 82, 88, 96, 100, 102, 106, 108, 112, 126, 130, 136, 138, 148, 150, 156, 162, 166, 172, 178, 180, 190, 192, 196, 198, 210, 222, 226, 228, 232, 238, 240, 250, 256, 262, 268, 270, 276

Offset

1,2

Comments

n-(-1)^n is prime.

Largest nonprime<prime(n+1) or largest nonprime<n-th odd prime. [From Juri-Stepan Gerasimov, Oct 29 2009]

Links

Table of n, a(n) for n=1..58.

Formula

A006093 \ {2}.

Example

k=1 is in the sequence because 1+1=2 is prime. k=4 is in the sequence because 1+4=5 is prime.

Mathematica

Select[Range[300], !PrimeQ[#]&&With[{d=Divisors[#]}, PrimeQ[d[[1]]+ d[[-1]]]]&] (* Harvey P. Dale, Oct 01 2015 *)

Crossrefs

Cf. A000040, A006093, A018252.

Sequence in context: A310577 A353465 A310578 * A156037 A089079 A310579

Adjacent sequences: A165969 A165970 A165971 * A165973 A165974 A165975

Keyword

nonn,less

Author

Juri-Stepan Gerasimov, Oct 02 2009, Oct 14 2009

Extensions

Entries checked by R. J. Mathar, Oct 10 2009

Status

approved