A371631 Primes whose product of nonzero digits divided by the sum of its digits is also prime.

167, 257, 523, 541, 617, 761, 1447, 1607, 1861, 2053, 2251, 2503, 2521, 2851, 4051, 5023, 5281, 5821, 6701, 8161, 8521, 10067, 10607, 10861, 11273, 11471, 12713, 13127, 13217, 13721, 14407, 16007, 17123, 17231, 17321, 18061, 20507, 20521, 21247, 21317, 21713, 22051

Offset: 1

Author

Mikk Heidemaa, May 24 2024

Keywords

• nonn
• base
• easy

Comments

No term N can have a "9" digit. [Proof: The sum of the digits of N is not a multiple of 3, but the numerator would be a multiple of 9, and so the number would be a multiple of 9, so not a prime.]

Examples

			167 (prime) is a term because 1*6*7/(1+6+7)=42/14=3 (prime).
		

Links

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

Crossrefs

Subsequence of A038367.

Equals prime terms of A138566.

Programs

Mathematica

pQ[n_] := Block[{idp = DeleteCases[IntegerDigits[n], 0]}, PrimeQ[Times @@ idp/Total@ idp]]; Cases[Prime@ Range@ PrimePi[10^5], _?pQ]
Select[Prime[Range[2500]],PrimeQ[Times@@(IntegerDigits[#]/.(0->1))/Total[ IntegerDigits[ #]]]&] (* Harvey P. Dale, Sep 24 2024 *)