A069917 - OEIS

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A069917

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

28, 145, 901, 1081 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,1`
	COMMENTS	`A number n is called "picture-perfect" if the reversal of n equals the sum of the reversals of the proper divisors of n. These base-6 picture-perfect numbers were found by Mark Ganson while searching for (base-10) picture-perfect numbers. He observes that the digital sum of their base-10 representations = 10 and conjectures that this is the case for all base-6 picture-perfect numbers. The only (base-10) picture-perfect numbers not exceeding 1.3 * 10^9 are 6, 10311 and 21661371.`
	LINKS	`Pe, J. The Picture-Perfect Numbers` `Systematic Undertaking to find Picture-Perfect Numbers Discussion Forum`
	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 base-6 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 A188778 A002593` `Adjacent sequences: A069914 A069915 A069916 * A069918 A069919 A069920`
	KEYWORD	`base,nonn`
	AUTHOR	`Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Apr 24 2002`

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Last modified February 15 23:53 EST 2012. Contains 205860 sequences.