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A247315
Numbers x such that the sum of all their cyclic permutations is equal to that of all cyclic permutations of sigma(x).
4
1, 15, 24, 69, 114, 133, 147, 153, 186, 198, 258, 270, 276, 288, 306, 339, 366, 393, 429, 474, 495, 507, 609, 627, 639, 717, 763, 817, 871, 1062, 1080, 1083, 1086, 1141, 1149, 1158, 1224, 1257, 1266, 1267, 1278, 1305, 1339, 1356, 1374, 1377, 1386, 1431, 1446
OFFSET
1,2
LINKS
EXAMPLE
The sum of the cyclic permutations of 153 is 153 + 315 + 531 = 999; sigma(153) = 234 and the sum of its cyclic permutations is 234 + 423 + 342 = 999.
The sum of the cyclic permutations of 4731 is 4731 + 1473 + 3147 + 7314 = 16665; sigma(4731) = 6720 and the sum of its cyclic permutations is 6720 + 672 + 2067 + 7206 = 16665.
MAPLE
with(numtheory):P:=proc(q) local a, b, c, d, k, n;
for n from 1 to q do a:=n; b:=a; c:=ilog10(a);
for k from 1 to c do a:=(a mod 10)*10^c+trunc(a/10); b:=b+a; od;
a:=sigma(n); d:=a; c:=ilog10(a);
for k from 1 to c do a:=(a mod 10)*10^c+trunc(a/10); d:=d+a; od;
if d=b then print(n); fi; od; end: P(10^9);
MATHEMATICA
scp[n_]:=Total[FromDigits/@Table[RotateRight[IntegerDigits[n], k], {k, IntegerLength[ n]}]]; Select[Range[1500], scp[#] == scp[DivisorSigma[ 1, #]]&] (* Harvey P. Dale, Nov 08 2020 *)
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Paolo P. Lava, Sep 12 2014
STATUS
approved