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 A241207 Consider a number of k digits n = d_(k)*10^(k-1) + d_(k-1)*10^(k-2) + … + d_(2)*10 + d_(1). Sequence lists the numbers n such that sigma(n)-n =  Sum_{i=1..k-1}{sigma(Sum_{j=1..i}{d_(j)*10^(j-1)})}} - Sum_{i=1..k-1}{sigma(Sum_{j=1..i}{d_(k-j+1)*10^(i-j)})} (see example below) 7
 23, 47, 142, 161, 433, 1435, 1900, 6679, 48917, 197943, 257941, 3916321, 48635983, 1142976889, 1811878288 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(16) > 10^10. - Giovanni Resta, May 23 2016 LINKS EXAMPLE If n = 48917, starting from the least significant digit, let us cut the number into the set 7, 17, 917, 8917. We have: sigma(7) = 8; sigma(17) = 18; sigma(917) = 1056; sigma(8917) = 9196. Then, starting from the most significant digit, let us cut the number into the set 4, 48, 489, 4891. We have: sigma(4) = 7; sigma(48) = 124; sigma(489) = 656; sigma(4891) = 5032. Finally, 8 + 18 + 1056 + 9196 - (7 + 124 + 656 + 5032) = 4459 = sigma(48917) - 48917. MAPLE with(numtheory); P:=proc(q) local a, b, k, n; for n from 2 to q do a:=0; k:=1; while trunc(n/10^k)>0 do a:=a+phi(trunc(n/10^k)); k:=k+1; od; b:=0; k:=1; while (n mod 10^k)

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Last modified September 18 07:57 EDT 2019. Contains 327168 sequences. (Running on oeis4.)