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A138572
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Numbers k that divide the sum of the digits of k^k in base 2.
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1
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1, 6, 122, 2126, 7910, 8254, 16201, 32312, 32426, 32998, 65436, 261649, 261803, 1044017, 1050183, 4194999
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OFFSET
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1,2
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COMMENTS
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Conjecture: the sequence is infinite.
The quotients are 1, 1, 3, 5, 6, 6, 7, 6, 7, 7, 7, 9, 9, 10, 10, 11.
a(17) > 4500000.
Observation: the known terms of this sequence are near a power of 2:
k log_2(k)
1 0.000000
6 2.584963
122 6.930737
2126 11.053926
7910 12.949462
8254 13.010878
16201 13.983795
32312 14.979782
32426 14.984863
32998 15.010091
65436 15.997797
261649 17.997273
261803 17.998122
1044017 19.993714
1050183 20.002209
4194999 22.000239
Searching near 2^23, 2^24, and 2^25 finds term 16783381.
(End)
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LINKS
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EXAMPLE
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6^6 = 1011011001000000_2; 1+0+1+1+0+1+1+0+0+1+0+0+0+0+0+0 = 6; 6 mod 6 = 0.
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MATHEMATICA
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Select[Range[1100000], Divisible[Total[IntegerDigits[#^#, 2]], #]&] (* Harvey P. Dale, Dec 18 2014 *)
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PROG
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(PARI) isok(k) = !(hammingweight(k^k) % k); \\ Michel Marcus, Aug 20 2021
(C) See Links section.
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CROSSREFS
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KEYWORD
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base,hard,more,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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