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A229211 Numbers k such that Sum_{j=1..k} (j*(j+1)/2 - sigma(j))^j == 0 (mod k), where sigma(j) = A000203(j) and j*(j+1)/2 - sigma(j) = A024816(j). 5
1, 2, 9, 78, 3205, 5589, 14153 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Tested up to k = 50000.

LINKS

Table of n, a(n) for n=1..7.

EXAMPLE

(1*2 / 2 - sigma(1))^1 + (2*3 / 2 - sigma(2))^2 + ... + (9*10 / 2 - sigma(10))^9 = 35223475538772 and 35223475538772 / 9 = 3913719504308.

MAPLE

with(numtheory); P:=proc(q) local n, t; t:=0;

for n from 1 to q do t:=t+(n*(n+1)/2-sigma(n))^n; if t mod n=0 then print(n); fi; od; end: P(10^6);

PROG

(PARI) isok(n) = sum(i=1, n, (i*(i+1)/2 - sigma(i))^i) % n == 0; \\ Michel Marcus, Nov 09 2014

CROSSREFS

Cf. A000203, A227427, A227429, A227502, A227848, A229095, A229207-A229210.

Sequence in context: A166891 A184894 A111196 * A056918 A194471 A215629

Adjacent sequences:  A229208 A229209 A229210 * A229212 A229213 A229214

KEYWORD

nonn,more

AUTHOR

Paolo P. Lava, Sep 16 2013

EXTENSIONS

Typo in name and crossref corrected by Michel Marcus, Nov 09 2014

STATUS

approved

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Last modified April 20 19:13 EDT 2021. Contains 343137 sequences. (Running on oeis4.)