A371631 - OEIS

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

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OFFSET

1,1

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.]

LINKS

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

EXAMPLE

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

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 *)

CROSSREFS

Subsequence of A038367.

Equals prime terms of A138566.

Sequence in context: A338343 A142329 A088291 * A140003 A015992 A065216

Adjacent sequences: A371628 A371629 A371630 * A371632 A371633 A371634

KEYWORD

nonn,base,easy

AUTHOR

Mikk Heidemaa, May 24 2024

STATUS

approved