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A114135
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Primitive numbers n such that the sums of the digits of n, n^2 and n^3 coincide (cf. A111434).
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4
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1, 468, 585, 5851, 5868, 28845, 58968, 21688965, 29588877, 37848897, 49879981, 58577797, 79898994, 79958368, 79979698, 89757468, 109699677, 159699969, 468957888, 479597652, 479896587, 480749985, 494899398, 497349981, 498678256
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OFFSET
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1,2
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COMMENTS
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Members of A111434 not congruent to 0 (mod 10). If k is a member of A111434 then so is 10^e*k.
The authors have calculated all members below 10^11.
The number of members less than 10^n {n=0..11}: 0,1,1,3,5,7,7,7,16,34,57,125.
Number of members congruent to k (mod 10): 0,7,1,0,2,23,8,20,49,15. But more interesting, number of members are congruent to k (mod 9): 66,59,0,0,0,0,0,0,0.
A007953(n) == n mod 9. Since 0 and 1 are the only k in [0,1,...8] with k == k^2 mod 9, all terms are congruent to 0 or 1 mod 9. - Robert Israel, Jan 26 2015
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LINKS
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MATHEMATICA
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sod[n_] := Plus @@ IntegerDigits@n; lst = {}; Do[ If[(Mod[n, 9] == 0 || Mod[n, 9] == 1) && Mod[n, 10] != 0 && sod@n == sod[n2] == sod[n3], AppendTo[lst, n]], {n, 108/2}]; lst
Select[Range[5*10^8], Length[Union[Total/@IntegerDigits/@{#, #^2, #^3}]]==1 && Mod[#, 10]!=0&] (* Harvey P. Dale, Jul 07 2020 *)
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PROG
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(PARI) isok(n) = (n % 10) && ((sd=sumdigits(n)) == sumdigits(n^2)) && (sd == sumdigits(n^3)); \\ Michel Marcus, Jan 20 2015
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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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STATUS
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approved
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