A067598 Decimal encoding of the prime factorization of n is a multiple of n.

21, 36, 8277, 22987, 31199, 59577, 2092101, 25224589, 29963201, 564423629, 1353149983, 30011570617, 37090609821, 392629311959

Offset: 1

Author

Joseph L. Pe, Jan 31 2002

Keywords

• base
• easy
• nonn

Comments

If n = p_1^e_1 * ... * p_r^e_r with p_1 < ... < p_r, then the decimal encoding is p_1 e_1...p_r e_r. For example, 15 = 3^1 * 5^1, so has decimal encoding 3151.

a(12) > 10^10. [From Donovan Johnson, Mar 26 2010]

a(15) > 10^12. - Giovanni Resta, Aug 17 2016

Examples

			The prime factorization of 21 = 3^1 * 7^1 with corresponding encoding 3171. 3171 = 21 * 151, a multiple of 21. So 21 is a term of the sequence.
		

Programs

Mathematica

Select[Range[100000], Mod[FromDigits[Flatten[IntegerDigits /@ Flatten[FactorInteger[ # ]]]], # ] ==0 &]

PARI

{a067598(a,b) = local(n,v); for(n=max(2,a),b,v=factor(n); if(eval(concat(vector(matsize(v)[1],k,concat(vector(matsize(v)[2],j,Str(v[k,j]))))))%n==0,print1(n,",")))}

Extensions

Edited and extended by Robert G. Wilson v, Feb 02 2002

Two more terms from Klaus Brockhaus, Feb 20 2002

a(10)-a(11) from Donovan Johnson, Mar 26 2010

a(12)-a(14) from Giovanni Resta, Aug 17 2016