A131101 Numbers that when added it to their prime factors +1 the result is a prime number, member of A131102.

1, 2, 3, 5, 11, 23, 27, 29, 30, 32, 36, 41, 53, 60, 66, 75, 78, 83, 89, 113, 114, 117, 130, 131, 132, 138, 140, 171, 173, 175, 179, 186, 191, 204, 220, 233, 239, 240, 246, 251, 255, 258, 260, 276, 279, 281, 285, 286, 293, 308, 310, 325, 338, 340, 354, 359, 363

Offset: 1

Author

Tomas Xordan, Jun 14 2007

Keywords

• easy
• nonn

Comments

The Sophie Germain prime numbers (A005384) are part of this sequence because when adding to one of them its only prime factor (itself) + 1 = 2*A005384 + 1 the result is another prime number (A005385)

Prime factors taken with multiplicity. - Harvey P. Dale, Sep 04 2024

Examples

			a(8)=29 because 29 + its only prime factor (itself) + 1 = 29+29+1= 59, and 59 is a prime number = A131102(8) = A005385(6).
a(9)=30 because 30 + its prime factors + 1 = 30 +(2+3+5)+1 =41, and 41 is a prime number = A131102(9).
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Programs

Mathematica

Select[Range[400],PrimeQ[Total[Times@@@FactorInteger[#]]+#+1]&] (* Harvey P. Dale, Sep 04 2024 *)

Formula

a(n)+ prime factors of a(n) + 1 = p ; p is a prime number, member of A131102.