A203615 Reversal of sigma(n) equals the sum of the reversals of the divisors of n.
1, 2, 3, 4, 5, 7, 21, 938, 17797, 44045, 87001, 454085, 2217425, 8156450, 8475789, 3293216050, 11130063842, 44662814795, 77084972662
Offset: 1
Examples
n=17797. Divisors: 1, 13, 37, 481, 1369, 17797. Sum of the reversals of the divisors: 1+31+73+184+9631+79771=89691. Sigma(17797)=19698 and its reversal is 89691. n=454085. Divisors: 1, 5, 197, 461, 985, 2305, 90817, 454085. Sum of the reversals of the divisors: 1+5+791+164+589+5032+71809+580454=658845. Sigma(454085)=548856 and its reversal is 658845.
Programs
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Maple
with(numtheory); Rev:=proc(n) local a, i, k; i:=convert(n,base,10); a:=0; for k from 1 to nops(i) do a:=a*10+i[k]; od; a; end: P:=proc(s) local a, b, c, j, pfs; for j from 1 to s do b:=divisors(j); a:=0; for c from 1 to nops(b) do a:=a+Rev(b[c]); od; if Rev(sigma(j))=a then print(j); fi; od; end: P(10000000);
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Mathematica
Select[Range[33*10^8],Total[IntegerReverse/@Divisors[#]] == IntegerReverse[ DivisorSigma[ 1,#]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 09 2018 *)
Extensions
a(13)-a(16) from Donovan Johnson, Jan 29 2012
a(17)-a(19) from Giovanni Resta, Aug 30 2018
Comments