

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.
a(6) > 10^8.  Amiram Eldar, Sep 28 2019
a(9) > 2*10^11.  Giovanni Resta, Sep 29 2019


LINKS

Table of n, a(n) for n=1..8.
J. Pe, The PicturePerfect Numbers


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

Sequence in context: A042530 A042532 A187608 * A028380 A219887 A271636
Adjacent sequences: A069914 A069915 A069916 * A069918 A069919 A069920


KEYWORD

base,nonn,more


AUTHOR

Joseph L. Pe, Apr 24 2002


EXTENSIONS

Corrected a link.  Alan T. Koski, Nov 25 2012
a(5) from Amiram Eldar, Sep 28 2019
a(6)a(8) from Giovanni Resta, Sep 29 2019


STATUS

approved



