A331093 Numbers such that the sum of their divisors, excluding 1 and the number itself, minus the sum of their digits equals the number.

12, 114256, 6988996, 8499988, 8689996, 8789788, 8877988, 8988868, 8999956, 9696988, 9759988, 9899596, 9948988, 9996868, 9998884, 9999892, 15996988, 16878988, 17799796, 17887996, 17988796, 17999884, 18579988, 18768988, 18869788, 18895996, 18958996, 18995788, 19398988, 19587988, 19698868, 19777996, 19799668

Offset

1,1

Comments

After the second term, it seems that the digit sum is 55.

All terms after a(2) appear to be of the form 2^2 * 7 * p, where p is a prime. - Scott R. Shannon, Jan 09 2020

If there exists a third term not of the form 2^2*7*p, it is larger than 10^13. - Giovanni Resta, Jan 14 2020

Links

Table of n, a(n) for n=1..33.

Example

a(3) = 6988996 as the sum of the divisors of 6988996, excluding 1 and 6988996, equals 6989051, the sum of its digits equals 55, and 6989051 - 55 = 6988996.

Mathematica

Select[Range[10^7], DivisorSigma[1, #] - Plus @@ IntegerDigits[#] == 2 # + 1 &] (* Amiram Eldar, Jan 08 2020 *)

Prog

(PARI) isok(n) = sigma(n) - n - 1 - sumdigits(n) == n; \\ Michel Marcus, Jan 09 2020

Crossrefs

Cf. A000203, A007953, A048050.

Cf. A331037 (sum of divisors + digit sum = number).

Sequence in context: A051368 A103482 A056540 * A369523 A328992 A069048

Adjacent sequences: A331090 A331091 A331092 * A331094 A331095 A331096

Keyword

nonn,base,less

Author

Joseph E. Marrow, Jan 08 2020

Extensions

Terms a(7) and beyond from Scott R. Shannon, Jan 09 2020

Status

approved