A163122 Composite numbers for which the sum of proper divisors equals the sum of the digit-reversed proper divisors.

4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 21, 22, 25, 27, 33, 35, 44, 49, 55, 66, 77, 88, 99, 121, 202, 242, 262, 302, 303, 362, 363, 382, 393, 403, 404, 453, 484, 505, 524, 543, 573, 605, 606, 626, 655, 689, 706, 707, 726, 746, 755, 766, 783, 786, 808, 840, 847, 905

Offset: 1

Author

Claudio Meller, Jul 21 2009

Keywords

• nonn
• base

Examples

			840 is in the sequence: the sum of its proper divisors is
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 10 + 12 + 14 + 15 + 20 + ... + 280 + 420 = A001065(840) = 2040,
and the sum of the reversed proper divisors is
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 1 + 21 + 41 + 51 + 2 + ... + 82 + 24 = A069250(840) = 2040.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Programs

Maple

read("transforms") ; A001065 := proc(n) numtheory[sigma](n)-n ; end:
A069250 := proc(n) local pdvs ,a,d ; pdvs := numtheory[divisors](n) minus {n} ; a := 0 ; for d in pdvs do a := a+digrev(d) ; od: a ; end:
for n from 4 to 1000 do if not isprime(n) and A001065(n) = A069250(n) then printf("%d,",n) ; fi; od: # R. J. Mathar, Jul 27 2009

Mathematica

Select[Range[1000],CompositeQ[#]&&DivisorSigma[1,#]-#==Total[IntegerReverse/@ Most[ Divisors[ #]]]&] (* Harvey P. Dale, Oct 12 2023 *)

Formula

{n : n in A002808, and A001065(n) = A069250(n)}. - R. J. Mathar, Jul 27 2009

Extensions

Keyword:base added by R. J. Mathar, Jul 27 2009