A024934 Sum of remainders n mod p, over all primes p < n.

0, 0, 0, 1, 1, 3, 1, 4, 6, 7, 4, 8, 8, 13, 10, 8, 12, 18, 20, 27, 28, 26, 21, 29, 33, 37, 31, 37, 37, 46, 46, 56, 65, 62, 54, 53, 59, 70, 61, 57, 62, 74, 75, 88, 89, 95, 84, 98, 108, 116, 124, 119, 119, 134, 145, 145, 152, 146, 131, 147, 154, 171, 156, 164, 180, 180, 182, 200, 200, 193, 198, 217

Offset

0,6

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Formula

a(n) = n*A000720(n) - A024924(n). - Max Alekseyev, Feb 10 2012

a(n) = a(n-1) + A000720(n-1) - A105221(n). - Max Alekseyev, Nov 28 2017

Example

a(5) = 3. The remainder when 5 is divided by primes 2, 3 respectively is 1, 2, and their sum = 3.
10 = 2*5+0 = 3*3+1 = 5*2+0 = 7*1+3: a(10) = 0+1+0+3 = 4.

Mathematica

a[n_] := Sum[Mod[n, Prime[i]], {i, PrimePi@ n}]; Array[a, 72, 0] (* Giovanni Resta, Jun 24 2016 *)

Prog

(PARI) a(n)=my(r=0); forprime(p=2, n, r+=n%p); r; \\ Joerg Arndt, Nov 05 2016

Crossrefs

Cf. A004125, A067435, A067436, A013939, A101336.

Sequence in context: A100954 A071315 A072267 * A186358 A170839 A049918

Adjacent sequences: A024931 A024932 A024933 * A024935 A024936 A024937

Keyword

nonn

Author

Clark Kimberling

Extensions

Edited by Max Alekseyev, Jan 30 2012

a(0)=0 prepended by Max Alekseyev, Dec 10 2013

Status

approved