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 A244069 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 Sum_{i=1..k-1}{phi(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). 3
 11, 21, 53, 75, 83, 95, 211, 506, 523, 708, 908, 932, 955, 1008, 5086, 6535, 7272, 7557, 9126, 20534, 31165, 51301, 52695, 71665, 73713, 85173, 90902, 93026, 93565, 210021, 313370, 330173, 406945, 423775, 521427, 633190, 728687, 850123, 926281 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS No single-digit terms are permitted. - Harvey P. Dale, Mar 08 2015 LINKS EXAMPLE If n = 423775, starting from the least significant digit, let us cut the number into the set {5, 75, 775, 3775, 23775}. We have: sigma(5) = 6; sigma(75) = 124; sigma(775) = 992; sigma(3775) = 4712; sigma(23775) = 39432. Then, starting from the most significant digit, let us cut the number into the set {4, 42, 423, 4237, 42377}. We have: phi(4) = 2; phi(42) = 12; phi(423) = 276; phi(4237) = 3996; phi(42377) = 40980. Finally, 6 + 124 + 992 + 4712 + 39432 = 2 + 12 + 276 + 3996 + 40980 = 45266. MAPLE with(numtheory); P:=proc(q) local a, b, k, n; for n from 10 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 July 15 22:48 EDT 2019. Contains 325061 sequences. (Running on oeis4.)