A259643 Numbers n such that sum of first n odd primes divides product of first n odd primes.

1, 3, 5, 11, 25, 29, 41, 49, 51, 59, 69, 81, 99, 103, 113, 131, 133, 135, 147, 149, 153, 181, 187, 193, 197, 199, 205, 211, 213, 217, 219, 229, 235, 239, 243, 255, 271, 277, 281, 287, 289, 303, 309, 313, 323, 333, 335, 343, 347, 357, 359, 365, 367, 381, 383, 389

Offset: 1

Author

Altug Alkan, Oct 02 2015

Keywords

• nonn
• easy

Comments

Obviously, a(n) is always an odd number.

Examples

			a(1) = 1 because prime(2) mod prime(2) = 3 mod 3 = 0.
a(2) = 3 because (prime(2) * prime(3) * prime(4)) mod (prime(2) + prime(3) + prime(4)) = 105 mod 15 = 0.
a(3) = 5 because (prime(2) * prime(3) * prime(4) * prime(5) * prime(6)) mod (prime(2) + prime(3) + prime(4) + prime(5) + prime(6)) = 15015 mod 39 = 0.
		

Crossrefs

Cf. A051838, A065091, A070826, A071089, A071148, A262807.

Programs

Mathematica

Module[{nn=400,op},op=Prime[Range[2,nn+1]];Select[Range[nn],Divisible[ Times@@ Take[op,#],Total[Take[op,#]]]&]] (* Harvey P. Dale, Nov 16 2022 *)