A098771 Numbers n such that sigma(n)=sigma(d_1)*sigma(d_2)*...*sigma(d_k) where d_1 d_2 ... d_k is the decimal expansion of n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 38, 58, 66, 87, 568, 766, 2799, 6478, 6785, 26486, 36685, 36893, 64788, 66758, 67586, 69664, 77686, 276895, 467683, 474668, 488973, 548678, 587667, 658648, 666369, 668954, 839666, 939669, 958968, 968765, 2386698

Offset: 1

Author

Farideh Firoozbakht, Oct 03 2004

Keywords

• base
• nonn

Comments

Number of terms of this sequence up to 15000000 is 72. Has this sequence at least one multi-digit prime term?

Examples

			97888745 is in the sequence because sigma(97888745) = 117936000 = sigma(9)*sigma(7)*sigma(8)*sigma(8)*sigma(8)*sigma(7)*sigma(4)*sigma(5).
		

Crossrefs

Cf. A098684, A098685.

Programs

Mathematica

Do[If[h=IntegerDigits[n];l=Length[h];!MemberQ[h, 0]&&DivisorSigma[ 1, n]==Product[DivisorSigma[1, h[[k]]], {k, l}], Print[n]] {n, 100000000}]
Select[Range[24*10^5],DivisorSigma[1,#]==Times@@DivisorSigma[1, IntegerDigits[ #]]&] (* Harvey P. Dale, Mar 07 2018 *)