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

1,2

Comments

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

Links

Table of n, a(n) for n=1..40.

Example

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).

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 *)

Crossrefs

Cf. A098684, A098685.

Sequence in context: A257554 A270393 A257787 * A276810 A024659 A342442

Adjacent sequences: A098768 A098769 A098770 * A098772 A098773 A098774

Keyword

base,nonn

Author

Farideh Firoozbakht, Oct 03 2004

Status

approved