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A138572 Numbers k that divide the sum of the digits of k^k in base 2. 0
1, 6, 122, 2126, 7910, 8254, 16201, 32312, 32426, 32998, 65436, 261649, 261803, 1044017, 1050183 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Conjecture: the sequence is infinite.

The quotients are 1, 1, 3, 5, 6, 6, 7, 6, 7, 7, 7, 9, 9, 10, 10.

LINKS

Table of n, a(n) for n=1..15.

EXAMPLE

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.

MATHEMATICA

Select[Range[1100000], Divisible[Total[IntegerDigits[#^#, 2]], #]&] (* Harvey P. Dale, Dec 18 2014 *)

PROG

(PARI) isok(k) = !(hammingweight(k^k) % k); \\ Michel Marcus, Aug 20 2021

CROSSREFS

Cf. A108827.

Sequence in context: A336808 A296801 A249168 * A078261 A239752 A193223

Adjacent sequences:  A138569 A138570 A138571 * A138573 A138574 A138575

KEYWORD

base,hard,more,nonn

AUTHOR

Robert Gerbicz, May 12 2008

EXTENSIONS

a(12)-a(15) from Lars Blomberg, Jul 01 2011

STATUS

approved

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Last modified May 18 10:28 EDT 2022. Contains 353807 sequences. (Running on oeis4.)