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 A154586 Numbers n for which abs((-1)^k*Sum_{k=1..n} ((n-k+1) mod k)) = 0. 1
 1, 4, 8, 25, 27, 75, 209, 3507, 8466, 16179, 29285, 33987, 175904, 326764, 1161207 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Subset of A154585. a(16) > 10^7. - Donovan Johnson, Oct 03 2011 LINKS FORMULA abs{(-1)^k*A004125} = 0 {a(n): A154585(a(n))=0}. - R. J. Mathar, Jan 14 2009 EXAMPLE n=8 -> abs(-(8 mod 1) + (7 mod 2) - (6 mod 3) + (5 mod 4) - (4 mod 5) + (3 mod 6) - (2 mod 7) + (1 mod 8)) = abs(-0 + 1 - 0 + 1 - 4 + 3 - 2 + 1) = abs(0) = 0. MAPLE P:=proc(i) local a, n; for n from 1 to i do a:=abs(add((-1)^k*((n-k+1) mod k), k=1..n)); if a=0 then print(n); fi; od; end: P(100); PROG (C) #include int main(int argc, char * argv[]) { for(int n=1;; n++) { unsigned long long a = 0; for(int k=1; k <=n; k += 2) a -= (n-k+1) % k ; for(int k=2; k <=n; k += 2) a += (n-k+1) % k ; if ( a == 0) printf("%d, \n", n) ; } } /* R. J. Mathar, Jan 14 2009 */ CROSSREFS Cf. A004125, A154585. Sequence in context: A090896 A131637 A163143 * A185615 A068367 A292548 Adjacent sequences:  A154583 A154584 A154585 * A154587 A154588 A154589 KEYWORD more,nonn AUTHOR Paolo P. Lava and Giorgio Balzarotti, Jan 12 2009 EXTENSIONS 8466 inserted, and sequence extended up to a(13), by R. J. Mathar, Jan 14 2009 a(14)-a(15) from Donovan Johnson, Oct 03 2011 STATUS approved

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Last modified September 23 14:40 EDT 2021. Contains 347618 sequences. (Running on oeis4.)