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A269308
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Consider a number x. Take the sum of its digits. Repeat the process deleting the first addendum and adding the previous sum. The sequence lists the numbers that after some iterations reach the sum of the divisors of x.
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5
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20, 25, 43, 44, 49, 59, 122, 206, 2485, 11899, 17608, 24141, 56207, 195236, 2424613, 2842925, 6241233, 59087970, 111205290, 124735931, 224269761, 1086241193
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OFFSET
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1,1
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COMMENTS
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44 works in both directions: n -> sigma(n) and sigma(n) -> n. See A269307.
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LINKS
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EXAMPLE
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sigma(20) = 42 : 2 + 0 = 2; 0 + 2 = 2; 2 + 2 = 4; 2 + 4 = 6; 4 + 6 = 10; 6 + 10 = 16; 10 + 16 = 26; 16 +26 = 42.
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MAPLE
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with(numtheory): P:=proc(q, h) local a, b, k, n, t, v; v:=array(1..h);
for n from 2 to q do a:=n; b:=ilog10(a)+1; if b>1 then
for k from 1 to b do v[b-k+1]:=(a mod 10); a:=trunc(a/10); od; t:=b+1; v[t]:=add(v[k], k=1..b);
while v[t]<sigma(n) do t:=t+1; v[t]:=add(v[k], k=t-b..t-1); od;
if v[t]=sigma(n) then print(n); fi; fi; od; end: P(10^6, 1000);
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MATHEMATICA
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Select[Range[10, 10^5], (s = DivisorSigma[1, #]; d = IntegerDigits[#]; While[Total[d] < s, d = Join[Rest[d], {Total[d]}]]; Total[d] == s) &] (* Robert Price, May 21 2019 *)
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CROSSREFS
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KEYWORD
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nonn,base,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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