A247315 Numbers x such that the sum of all their cyclic permutations is equal to that of all cyclic permutations of sigma(x).

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

Author

Paolo P. Lava, Sep 12 2014

Keywords

• nonn
• base
• easy

Examples

			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.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000203, A247316, A247317.

Programs

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 *)