

A069917


In base 6, the reversal of n equals the sum of the reversals of the proper divisors of n.


0




OFFSET

1,1


COMMENTS

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.


LINKS



EXAMPLE

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.


MATHEMATICA

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}]


CROSSREFS



KEYWORD

base,nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



