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A331093
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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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2
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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Select[Range[10^7], DivisorSigma[1, #] - Plus @@ IntegerDigits[#] == 2 # + 1 &] (* Amiram Eldar, Jan 08 2020 *)
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PROG
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(PARI) isok(n) = sigma(n) - n - 1 - sumdigits(n) == n; \\ Michel Marcus, Jan 09 2020
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CROSSREFS
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Cf. A331037 (sum of divisors + digit sum = number).
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KEYWORD
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nonn,base,less
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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