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A331096
Numbers k such that the sum of all divisors except k, minus the sum of the digits of k, is equal to k.
2
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
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
KEYWORD
nonn,base,less
AUTHOR
Joseph E. Marrow, Jan 08 2020
STATUS
approved