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A333622
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Numbers k such that k is divisible by the sum of digits of all the divisors of k in factorial base (A319712).
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2
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1, 2, 3, 4, 14, 22, 24, 27, 33, 36, 52, 72, 91, 92, 100, 135, 150, 187, 221, 231, 310, 323, 448, 481, 493, 494, 589, 663, 708, 754, 816, 884, 893, 897, 946, 1080, 1155, 1159, 1178, 1200, 1357, 1462, 1475, 1518, 1530, 1536, 1550, 1702, 1710, 1836, 1972, 1978, 2231
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OFFSET
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1,2
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LINKS
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EXAMPLE
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14 is a term since its divisors are {1, 2, 7, 14}, their representations in factorial base (A007623) are {1, 10, 101, 210}, and their sum of sums of digits is 1 + (1 + 0) + (1 + 0 + 1) + (2 + 1 + 0) = 7 which is a divisor of 14.
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MATHEMATICA
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fctDigSum[n_] := Module[{s=0, i=2, k=n}, While[k > 0, k = Floor[n/i!]; s = s + (i-1)*k; i++]; n-s]; fctDivDigDum[n_] := DivisorSum[n, fctDigSum[#] &]; Select[Range[10^3], Divisible[#, fctDivDigDum[#]] &] (* after Jean-François Alcover at A034968 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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