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A328446 Table read by rows: the n-th row gives the nonnegative integers k such that n - k is a power of k.

%I A328446 #17 Oct 17 2019 02:01:52
%S A328446 0,1,2,2,3,4,2,3,5,6,4,7,8,2,5,9,10,3,6,11,12,7,13,14,8,15,16,2,9,17,
%T A328446 18,4,10,19,20,11,21,22,12,23,24,13,25,26,14,27,28,3,5,15,29,30,16,31,
%U A328446 32,2,17,33,34,18,35,36,19,37,38,20,39,40,6,21,41,42,22
%N A328446 Table read by rows: the n-th row gives the nonnegative integers k such that n - k is a power of k.
%C A328446 The n-th row has length A309978(n) for n > 1.
%H A328446 Peter Kagey, <a href="/A328446/b328446.txt">Table of n, a(n) for n = 1..10000</a>
%e A328446 Table begins
%e A328446    n | n-th row
%e A328446   ---+----------
%e A328446    1 | 0
%e A328446    2 | 1
%e A328446    3 | 2
%e A328446    4 | 2, 3
%e A328446    5 | 4
%e A328446    6 | 2, 3, 5
%e A328446    7 | 6
%e A328446    8 | 4, 7
%e A328446    9 | 8
%e A328446   10 | 2, 5, 9
%e A328446   11 | 10
%e A328446   12 | 3, 6, 11
%e A328446   13 | 12
%e A328446   14 | 7, 13
%e A328446   15 | 14
%e A328446   16 | 8, 15
%e A328446   17 | 16
%e A328446   18 | 2, 9, 17
%e A328446 For n = 10 the 10th row is 2, 5, 9 because
%e A328446 10 - 2 = 2^3,
%e A328446 10 - 5 = 5^1, and
%e A328446 10 - 9 = 9^0.
%o A328446 (PARI) row(n) = {if (n==1, return ([0])); my(row = vector(0)); fordiv(n, d, if ((d>1) && (d<n) && (d^valuation(n-d, d) == n-d), row = concat(row, d))); concat(row, n-1);}
%o A328446 tabf(nn) = {for (n=1, nn, print(row(n)););} \\ _Michel Marcus_, Oct 16 2019
%Y A328446 Cf. A307092, A309978.
%K A328446 nonn,tabf
%O A328446 1,3
%A A328446 _Peter Kagey_, Oct 15 2019