A375788 Prime numbers such that the product of their digits is a highly composite number.

2, 11, 23, 41, 43, 61, 83, 149, 211, 223, 229, 263, 283, 419, 431, 433, 443, 461, 491, 641, 661, 823, 853, 859, 941, 1123, 1213, 1223, 1229, 1231, 1283, 1321, 1381, 1423, 1433, 1453, 1459, 1543, 1549, 1583, 1621, 1823, 1831, 1861, 2111, 2113, 2129, 2131, 2143

Offset

1,1

Links

Table of n, a(n) for n=1..49.

Mathematica

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 *)

Prog

(Python)
from math import *
from sympy import *
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
digits = []
result = 1
for i in range(100000):#the 100000 in here is what you'll want to change to get more of these numbers
    result = 1
    if isprime(i) == True:
        digits = [*str(i)]
        for j in range(len(str(i))):
            result = result*int(digits[j])
        for k in numbers:
            if result == k:
                print(i)

Crossrefs

Cf. A002182.

Sequence in context: A106856 A045387 A103255 * A031385 A294551 A179878

Adjacent sequences: A375785 A375786 A375787 * A375789 A375790 A375791

Keyword

nonn,base

Author

Edoardo Sangiuliano, Aug 28 2024

Extensions

More terms from Amiram Eldar, Aug 29 2024

Status

approved