A331098 The numbers such that the sum of their proper divisors minus the product of their digits equals the number.

198, 4172, 7144, 27824, 72212, 111126, 1111134, 1113114, 1131114, 7121212, 11131122, 13111122, 33550336, 111711124, 1111113114, 1111212172, 1113111114, 2111211172, 7111211212, 8589869056, 11112117212, 11113111122, 11121121172, 11711121212, 13111111122, 17112111212

Offset

1,1

Comments

The perfect numbers containing a 0 digit are all in this sequence.

Links

Giovanni Resta, Table of n, a(n) for n = 1..30 (terms < 10^13)

Example

198 is a term: A001065(198) = 270, A007954(198) = 72, and 270 - 72 - 198.
4172 is a term: A001065(4172) = 4228, A007954(4172) = 56, and 4228 - 56 = 4172.

Mathematica

Select[Range[10^6], DivisorSigma[1, #] - Times @@ IntegerDigits[#] == 2 # &] (* Amiram Eldar, Jan 18 2020 *)

Prog

(PARI) isok(n) = my(d=digits(n)); sigma(n) - n - vecprod(d) == n; \\ Michel Marcus, Jan 18 2020

Crossrefs

Cf. A001065, A007954, A331096.

Sequence in context: A364860 A224452 A227705 * A290933 A278017 A348602

Adjacent sequences: A331095 A331096 A331097 * A331099 A331100 A331101

Keyword

nonn,base,less

Author

Scott R. Shannon, Jan 09 2020

Extensions

a(13)-a(14) from Michel Marcus, Jan 18 2020

a(15)-a(26) from Giovanni Resta, Jan 18 2020

Status

approved