A152147
Irregular triangle in which row n lists k > 0 such that the sum of digits of k^n equals k.
Original entry on oeis.org
1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 9, 1, 8, 17, 18, 26, 27, 1, 7, 22, 25, 28, 36, 1, 28, 35, 36, 46, 1, 18, 45, 54, 64, 1, 18, 27, 31, 34, 43, 53, 58, 68, 1, 46, 54, 63, 1, 54, 71, 81, 1, 82, 85, 94, 97, 106, 117, 1, 98, 107, 108, 1, 108, 1, 20, 40, 86, 103, 104, 106, 107, 126, 134, 135
Offset: 1
1, 2, 3, 4, 5, 6, 7, 8, 9;
1, 9;
1, 8, 17, 18, 26, 27; (A046459, with 0)
1, 7, 22, 25, 28, 36; (A055575 " )
1, 28, 35, 36, 46; (A055576 " )
1, 18, 45, 54, 64; (A055577 " )
1, 18, 27, 31, 34, 43, 53, 58, 68; (A226971 " )
1, 46, 54, 63;
1, 54, 71, 81,
1, 82, 85, 94, 97, 106, 117,
1, 98, 107, 108, etc.
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def ok(k, r): return sum(map(int, str(k**r))) == k
def agen(rows, startrow=1, withzero=0):
for r in range(startrow, rows + startrow):
d, lim = 1, 1
while lim < r*9*d: d, lim = d+1, lim*10
yield from [k for k in range(1-withzero, lim+1) if ok(k, r)]
print([an for an in agen(13)]) # Michael S. Branicky, May 23 2021
A055577
Numbers k such that the sum of digits of k^6 is equal to k.
Original entry on oeis.org
0, 1, 18, 45, 54, 64
Offset: 1
a(2) = 18 because 18^6 = 34012224 and 3+4+0+1+2+2+2+4 = 18
A281918
7th power analog of Keith numbers.
Original entry on oeis.org
1, 18, 27, 31, 34, 43, 53, 58, 68, 145, 187, 314, 826, 2975, 37164, 40853, 58530, 72795, 77058, 160703, 187617, 1926759, 6291322, 6628695, 25285305, 31292514, 33968486, 54954185, 71593237, 125921697, 555963577, 575307142, 2393596216, 2444508547, 42544333760, 97812197525
Offset: 1
145^7 = 1347646586640625:
1 + 3 + 4 + 7 + 6 + 4 + 6 + 5 + 8 + 6 + 6 + 4 + 0 + 6 + 2 + 5 = 73;
3 + 4 + 7 + 6 + 4 + 6 + 5 + 8 + 6 + 6 + 4 + 0 + 6 + 2 + 5 + 73 = 145.
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with(numtheory): P:=proc(q, h,w) local a, b, k, t, v; global n; v:=array(1..h);
for n from 1 to q do b:=n^w; a:=[];
for k from 1 to ilog10(b)+1 do a:=[(b mod 10), op(a)]; b:=trunc(b/10); od;
for k from 1 to nops(a) do v[k]:=a[k]; od; b:=ilog10(n^w)+1;
t:=nops(a)+1; v[t]:=add(v[k], k=1..b); while v[t]
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(* function keithQ[ ] is defined in A007629 *)
a281918[n_] := Join[{1}, Select[Range[10, n], keithQ[#, 7]&]]
a281918[10^6] (* Hartmut F. W. Hoft, Jun 03 2021 *)
Showing 1-3 of 3 results.
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