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A229211
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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).
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5
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OFFSET
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1,2
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COMMENTS
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Tested up to k = 50000.
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LINKS
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EXAMPLE
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(1*2 / 2 - sigma(1))^1 + (2*3 / 2 - sigma(2))^2 + ... + (9*10 / 2 - sigma(10))^9 = 35223475538772 and 35223475538772 / 9 = 3913719504308.
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MAPLE
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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);
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PROG
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(PARI) isok(n) = sum(i=1, n, (i*(i+1)/2 - sigma(i))^i) % n == 0; \\ Michel Marcus, Nov 09 2014
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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Typo in name and crossref corrected by Michel Marcus, Nov 09 2014
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STATUS
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approved
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