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

6, 11, 778, 11735953

Offset

1,1

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). a(5) > 10^11. - Charles R Greathouse IV, Nov 03 2014

a(5) > 2*10^12. - Giovanni Resta, Aug 30 2018

Links

Table of n, a(n) for n=1..4.

Example

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

Mathematica

Do[If[DivisorSigma[1, n]-n==Apply[Times, IntegerDigits[n]], Print[n]], {n, 50000000}]

Prog

(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

Crossrefs

Subsequence of A052382.

Cf. A004022.

Sequence in context: A136980 A083834 A136978 * A024267 A028584 A243017

Adjacent sequences: A145743 A145744 A145745 * A145747 A145748 A145749

Keyword

base,more,nice,nonn

Author

Farideh Firoozbakht, Oct 27 2008

Status

approved