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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 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.)