A145746 Numbers k such that sum of the proper divisors of k is equal to the product of the digits of k.

6, 11, 778, 11735953, 33155353153393, 115399371137353, 3355195531177393, 3515999553551113, 15751375595175193, 19779913155711913, 773153371177599193, 1111111111111111111

Offset: 1

Author

Farideh Firoozbakht, Oct 27 2008

Keywords

• base
• more
• nice
• nonn

Comments

All repunit primes are in the sequence. So A004022 is a subsequence of this sequence.

All terms beyond a(3) are coprime to 6, and of course all terms are zerofree (A052382). - Charles R Greathouse IV, Nov 03 2014

Examples

			sigma(11735953) = sigma(883*13291) = 11735953 + (13291 + 883 + 1) = 11735953 + 1*1*7*3*5*9*5*3 so 11735953 is in the sequence.
		

Crossrefs

Subsequence of A052382.

Cf. A004022.

Programs

Mathematica

Do[If[DivisorSigma[1,n]-n==Apply[Times,IntegerDigits[n]],Print[n]], {n,50000000}]
Select[Range[800],DivisorSigma[1,#]-#==Times@@IntegerDigits[#]&] (* Harvey P. Dale, Dec 06 2024 *)

PARI

is(n)=my(d=digits(n),p=prod(i=1,#d,d[i])); p>0 && p+n==sigma(n) \\ Charles R Greathouse IV, Nov 03 2014

Extensions

Definition clarified by Harvey P. Dale, Dec 06 2024

a(5)-a(12) from Max Alekseyev, Jun 10 2025