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%I #13 Sep 22 2024 18:40:18
%S 2,11,23,41,43,61,83,149,211,223,229,263,283,419,431,433,443,461,491,
%T 641,661,823,853,859,941,1123,1213,1223,1229,1231,1283,1321,1381,1423,
%U 1433,1453,1459,1543,1549,1583,1621,1823,1831,1861,2111,2113,2129,2131,2143
%N Prime numbers such that the product of their digits is a highly composite number.
%t seq[digmax_] := Module[{hcn = Select[Import["https://oeis.org/A002182/b002182.txt", "Table"][[;; , 2]], # < 10^digmax &]}, Select[Prime[Range[PrimePi[10^digmax]]], MemberQ[hcn, Times @@ IntegerDigits[#]] &]]; seq[4] (* _Amiram Eldar_, Aug 29 2024 *)
%o (Python)
%o from math import *
%o from sympy import *
%o numbers =[1,2,4,6,12,24,36,48,60,120,180,240,360,720,840,1260,1680,2520,5040,7560,10080,15120,20160,25200,27720,45360,50400,55440]#this is the list of highly composite numbers
%o digits = []
%o result = 1
%o for i in range(100000):#the 100000 in here is what you'll want to change to get more of these numbers
%o result = 1
%o if isprime(i) == True:
%o digits = [*str(i)]
%o for j in range(len(str(i))):
%o result = result*int(digits[j])
%o for k in numbers:
%o if result == k:
%o print(i)
%Y Cf. A002182.
%K nonn,base
%O 1,1
%A _Edoardo Sangiuliano_, Aug 28 2024
%E More terms from _Amiram Eldar_, Aug 29 2024