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

Author

Scott R. Shannon, Jan 09 2020

Keywords

• nonn
• base
• less

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A001065, A007954, A331096.

Programs

Mathematica

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

PARI

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

Extensions

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

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