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

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

1,1

Comments

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

Links

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

Maple

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

Mathematica

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

Prog

(PARI) isok(k) = sigma(k) - k - sumdigits(k) == k; \\ Michel Marcus, Jan 11 2020
(Magma) [k:k in [1..8250]| DivisorSigma(1, k) eq 2*k+&+Intseq(k)]; // Marius A. Burtea, Jan 11 2020

Crossrefs

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

Related sequences are A331037 and A331093.

Sequence in context: A074632 A225190 A228839 * A304253 A330931 A158444

Adjacent sequences: A331093 A331094 A331095 * A331097 A331098 A331099

Keyword

nonn,base,less

Author

Joseph E. Marrow, Jan 08 2020

Status

approved