A154586 Numbers n for which abs((-1)^k*Sum_{k=1..n} ((n-k+1) mod k)) = 0.

1, 4, 8, 25, 27, 75, 209, 3507, 8466, 16179, 29285, 33987, 175904, 326764, 1161207

Offset

1,2

Comments

Subset of A154585.

a(16) > 10^7. - Donovan Johnson, Oct 03 2011

Links

Table of n, a(n) for n=1..15.

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 <stdio.h> 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 * A371190 A185615 A068367

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