%I #25 May 27 2024 19:58:40
%S 28,145,901,1081,1749715,153533665,159114735,182475267415
%N In base 6, the reversal of n equals the sum of the reversals of the proper divisors of n.
%C A number n is called "pictureperfect" if the reversal of n equals the sum of the reversals of the proper divisors of n. These base6 pictureperfect numbers were found by Mark Ganson while searching for (base10) pictureperfect numbers. He observes that the digital sum of their base10 representations = 10 and conjectures that this is the case for all base6 pictureperfect numbers. The only (base10) pictureperfect numbers not exceeding 1.3 * 10^9 are 6, 10311 and 21661371.
%C a(9) > 2*10^11.  _Giovanni Resta_, Sep 29 2019
%H J. Pe, <a href="http://www.numeratus.net/enlightened/pictureperfect.html">The PicturePerfect Numbers</a>
%e 28 has proper divisors 1, 2, 4, 7, 14. 28 = 44_6, 1 = 1_6, 2 = 2_6, 4 = 4_6, 7 = 11_6, 14 = 22_6. Reversing these base6 numbers, we have 44_6 = 1_6 + 2_6 + 4_6 + 11_6 + 22_6 so 28 belongs to the sequence.
%t base=6; f[n_] := FromDigits[Reverse[IntegerDigits[n, base]], base]; baseDivisors[n_, base_] := IntegerDigits[Drop[Divisors[n], 1], base]; Do[ startFrom = 2; Do[If[f[n] == Apply[Plus, Map[f, Drop[Divisors[n], 1]]], Print["base = ", base, ", n = ", n, ") ", IntegerDigits[n, base], " divisors: ", Drop[Divisors[n], 1], " base divisors: ", baseDivisors[n, base]]], {n, startFrom, 10000}], {base, 2, 10}]
%K base,nonn,more
%O 1,1
%A _Joseph L. Pe_, Apr 24 2002
%E a(5) from _Amiram Eldar_, Sep 28 2019
%E a(6)a(8) from _Giovanni Resta_, Sep 29 2019
