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A220365
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a(n) is conjectured to be the largest power k for which k divides the sum of digits of n^k.
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1
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1, 70, 486, 35, 10, 90, 805, 5218, 243, 1, 35, 1494, 469004, 1045, 288, 116, 7, 195, 29, 70, 16710, 23, 2, 1017, 28, 58, 162, 166, 209, 486, 205, 106, 1206, 2053, 37120
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OFFSET
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1,2
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COMMENTS
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a(36) >= 423378.
Please consult the argument in A067863 for the reason that it is believed that all individual such sequences (all k's which divide b^k) terminate.
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LINKS
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FORMULA
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If a(n) = k, then a(10*n) = k.
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EXAMPLE
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a(2) = 70 since the sum of digits of 2^70 is divisible by 70 and it is believed that there does not exist any larger exponent which satisfies this criterion.
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MATHEMATICA
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For any individual base, b, fQ[n_] := Mod[Plus @@ IntegerDigits[b^n], n] == 0; k = 1; lst = {}; While[k < 100001, If[ fQ@ k, AppendTo[lst, k]; Print[k]]; k++]; lst
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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