A241681 Numbers n such that the decimal digits of n are also the prime divisors of n.

2, 3, 5, 7, 735, 2333772

Offset: 1

Author

Michel Lagneau, Apr 27 2014

Keywords

• nonn
• base
• hard

Comments

The sequence is given for a(n) < 10^11.

No more terms <= 10^150. Terms are of the form 2^e2 * 3^e3 * 7^e7 or of the form 3^e3 * 5^e5 * 7^e7, for which no other number <= 10^150 than those listed is a term. - David A. Corneth, Sep 28 2019

No more terms <= 10^1000. - Michael S. Branicky, May 30 2025

Examples

			735 = 3*5*7^2 is in the sequence because the digits 7, 3 and 5 are also the prime divisors of 735.
		

Crossrefs

Cf. A108319, A108347.

Subsequence of A046034.

Programs

Maple

with(numtheory):nn:=1000000:for n from 1 to 10^11 do:lst:={}:x:=factorset(n):y:=convert(n,base,10):n1:=nops(x):n2:=nops(y): for j from 1 to n2 do:lst:=lst union {y[j]}:od:if x=lst then print(n):else fi:od: