A331037 -id:A331037 - cp's OEIS frontend

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

Joseph E. Marrow, Jan 08 2020

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

			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.

Cf. A000203, A007953, A048050.

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

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

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

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

A331096 Numbers k such that the sum of all divisors except k, minus the sum of the digits of k, is equal to k.

Original entry on oeis.org

20, 66, 138, 174, 246, 282, 318, 354, 426, 534, 606, 642, 822, 1038, 1074, 1146, 1182, 1362, 1434, 1506, 1542, 1614, 1902, 2082, 2118, 2154, 2334, 2406, 2514, 2802, 3018, 3054, 3126, 3342, 3414, 3522, 3702, 4062, 4206, 4314, 5034, 5142, 5322, 6114, 7122, 7232, 7302, 8202

Offset: 1

Joseph E. Marrow, Jan 08 2020

The first two odd elements are a(49) = 8415 and a(107) = 31815.- Robert Israel, Jan 16 2020

Robert Israel, Table of n, a(n) for n = 1..1400

Cf. A007953 (sum of digits), A001065 (sum of proper divisors).

Related sequences are A331037 and A331093.

[k:k in [1..8250]| DivisorSigma(1,k) eq 2*k+&+Intseq(k)]; // Marius A. Burtea, Jan 11 2020

filter:= proc(k) numtheory:-sigma(k)-convert(convert(k,base,10),`+`)=2*k end proc:
select(filter, [$1..10000]); # Robert Israel, Jan 16 2020

Select[Range[10^4], DivisorSigma[1, #] - Plus @@ IntegerDigits[#] == 2 # &] (* Amiram Eldar, Jan 11 2020 *)

isok(k) = sigma(k) - k - sumdigits(k) == k; \\ Michel Marcus, Jan 11 2020

cp's OEIS Frontend

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

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