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 A240902 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) 9
 39, 147, 413, 1268, 1550, 3964, 9987, 137097, 238268, 285993, 2139783, 4866838, 74523325, 131135109 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(15) > 10^10. - Giovanni Resta, May 23 2016 LINKS EXAMPLE If n = 238268, starting from the least significant digit, let us cut the number into the set 8, 68, 268, 8268, 38268. We have: sigma(8) = 15; sigma(68) = 126; sigma(268) = 476; sigma(8268) = 21168; sigma(38268) = 96824. Then, starting from the most significant digit, let us cut the number into the set 2, 23, 238, 2382, 23826. We have: sigma(2) = 3; sigma(23) = 24; sigma(238) = 432; sigma(2382) = 4776; sigma(23826) = 54864. Finally, 15 + 126 + 476 + 21168 + 96824 + 3 + 24 + 432 + 4776 + 54864 = 178708 = sigma(238268) - 238268. 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+sigma(trunc(n/10^k)); k:=k+1; od; b:=0; k:=1; while (n mod 10^k)

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Last modified March 26 18:36 EDT 2019. Contains 321511 sequences. (Running on oeis4.)