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%I #16 Aug 26 2019 05:23:21
%S 2,3,5,6,7,316,427,844,918,1671,2421,3526,4087,4757,10693,65230,
%T 181331,187739,351419,428461,480173,810413,874141,940561,1807139,
%U 2826223,2832833,2845121,3105547,3476531,3626369,3669571,3877163,4585571,6361571,6380653,6547379
%N Numbers whose sum of aliquot parts is equal to the sum of some fixed power of their digits.
%H Giovanni Resta, <a href="/A269670/b269670.txt">Table of n, a(n) for n = 1..3832</a> (terms < 10^12)
%H Paolo P. Lava, <a href="/A269670/a269670.txt">Terms of the sequence and their fixed power</a>
%F 2^0 = 1 and sigma(2) - 2 = 1;
%F 6^1 = 6 and sigma(6) - 6 = 6;
%F 3^3 + 1^3 + 6^3 = 244 and sigma(316) - 316 = 244.
%p with(numtheory); P:= proc(q) local a,b,c,d,k,n,ok; for n from 1 to q do d:=sigma(n)-n; a:=[]; b:=n; ok:=0;
%p for k from 1 to ilog10(n)+1 do if (b mod 10)>1 then ok:=1; fi; a:=[(b mod 10),op(a)]; b:=trunc(b/10); od; b:=-1; c:=0;
%p if ok=1 then while c<d do b:=b+1;
%p if b>0 then c:=add(a[k]^b, k=1..nops(a)); else for k from 1 to nops(a) do if a[k]=0 then c:=0; break; else c:=c+1; fi; od; fi; od; if c=d then print(n); fi; fi; od; end: P(10^9);
%o (PARI) isok(n)=vd = digits(n); if (vecmax(vd) <= 1, return (0)); sap = sigma(n) - n; k = 0; while ((sdj=sum(j=1, #vd, vd[j]^k)) < sap, k++); (sdj == sap); \\ _Michel Marcus_, Mar 04 2016
%Y Cf. A001065.
%K nonn,base
%O 1,1
%A _Paolo P. Lava_, Mar 03 2016
%E More terms from _Giovanni Resta_, Aug 26 2019
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