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A269670 Numbers whose sum of aliquot parts is equal to the sum of some fixed power of their digits. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A343742 A067077 A067183 * A333480 A036587 A075145

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

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Last modified September 19 12:18 EDT 2021. Contains 347556 sequences. (Running on oeis4.)