A269670 Numbers whose sum of aliquot parts is equal to the sum of some fixed power of their digits.

2, 3, 5, 6, 7, 316, 427, 844, 918, 1671, 2421, 3526, 4087, 4757, 10693, 65230, 181331, 187739, 351419, 428461, 480173, 810413, 874141, 940561, 1807139, 2826223, 2832833, 2845121, 3105547, 3476531, 3626369, 3669571, 3877163, 4585571, 6361571, 6380653, 6547379

Offset

1,1

Links

Giovanni Resta, Table of n, a(n) for n = 1..3832 (terms < 10^12)

Paolo P. Lava, Terms of the sequence and their fixed power

Formula

2^0 = 1 and sigma(2) - 2 = 1;

6^1 = 6 and sigma(6) - 6 = 6;

3^3 + 1^3 + 6^3 = 244 and sigma(316) - 316 = 244.

Maple

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;
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;
if ok=1 then while c<d do b:=b+1;
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);

Prog

(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

Crossrefs

Cf. A001065.

Sequence in context: A370688 A357132 A067183 * A333480 A373600 A377738

Adjacent sequences: A269667 A269668 A269669 * A269671 A269672 A269673

Keyword

nonn,base

Author

Paolo P. Lava, Mar 03 2016

Extensions

More terms from Giovanni Resta, Aug 26 2019

Status

approved