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Search: id:A128912
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| A128912 |
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Numbers n of form m^k, m>1, k>1, such that m = (sum of the digits of n). |
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| 81, 512, 2401, 4913, 5832, 17576, 19683, 234256, 390625, 614656, 1679616, 17210368, 34012224, 52521875, 60466176, 205962976, 612220032, 8303765625, 10460353203, 24794911296, 27512614111, 52523350144, 68719476736
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Perfect powers n > 1 such that the sum of the digits of n equals one of its nontrivial roots.
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EXAMPLE
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234256 = 22^4 and 2+3+4+2+5+6 = 22, hence 234256 is a term.
390625 = 25^4 and 3+9+0+6+2+5 = 25, hence 390625 is a term.
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PROGRAM
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(PARI) {digitsum(n) = local(s, d); s=0; while(n>0, d=divrem(n, 10); n=d[1]; s=s+d[2]); s} {m=1000000; z=1000000000000; v=[]; for(n=2, m, k=2; while((p=n^k)<=z, s=digitsum(p); if(n==s, v=concat(v, p)); k++)); v=vecsort(v); print(v)} /* Klaus Brockhaus, Apr 24 2007 */
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CROSSREFS
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Cf. A001597 (perfect powers).
Adjacent sequences: A128909 A128910 A128911 this_sequence A128913 A128914 A128915
Sequence in context: A008848 A102741 A017630 this_sequence A076090 A139156 A016756
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KEYWORD
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nonn,base
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AUTHOR
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J. M. Bergot (thekingfishb(AT)yahoo.ca), Apr 23 2007
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EXTENSIONS
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Edited, corrected and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Apr 24 2007
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