A331099 The numbers such that the sum of their proper divisors plus the product of their digits equals the number.

1, 14, 27, 154, 284, 574, 1264, 2588, 7288, 49852, 2342656, 33550336, 8589869056

Offset: 1

Author

Scott R. Shannon, Jan 09 2020

Keywords

• nonn
• base
• less
• more

Comments

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

a(14) > 10^13. - Giovanni Resta, Jan 19 2020

Examples

			14 is a term as A001065(14) = 10, A007954(14) = 4, and 10 + 4 = 14.
2588 is a term as A001065(2588) = 1948, A007954(2588) = 640, and 1948 + 640 = 2588.
		

Crossrefs

Cf. A001065, A007954, A331098.

Programs

Magma

[k:k in [1..2500000]| k eq &*Intseq(k)+DivisorSigma(1,k)-k]; // Marius A. Burtea, Jan 18 2020

Mathematica

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

PARI

isok(n) = my(d=digits(n)); sigma(n) + vecprod(d) == 2*n; \\ Jinyuan Wang, Jan 19 2020

Extensions

a(12) from Jinyuan Wang, Jan 19 2020

a(13) from Giovanni Resta, Jan 19 2020