A143853 -id:A143853 - cp's OEIS frontend

A233131 Sum of remainders of n modulo all smaller composite numbers.

0, 0, 0, 0, 0, 1, 2, 4, 2, 5, 9, 14, 9, 15, 21, 28, 24, 33, 27, 37, 33, 44, 56, 69, 52, 66, 81, 88, 87, 105, 92, 111, 102, 122, 143, 165, 139, 163, 187, 212, 196, 223, 209, 237, 239, 244, 274, 305, 266, 298, 296, 330, 335, 371, 347, 384, 368, 407, 447, 488, 432, 474, 516, 529, 513, 558, 543, 590, 599, 647, 637, 687, 620

Offset: 0

Max Alekseyev, Dec 07 2013

nonn

Cf. A143853, A233344

Table[Total[Mod[n,Select[Range[n-1],CompositeQ]]],{n,0,80}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 01 2018 *)

a(n) = A004125(n) - A024934(n).

A233344 Numbers k that divide the sum of their remainders modulo all smaller composites (=A233131(k)).

Original entry on oeis.org

1, 2, 3, 4, 23, 53, 374, 613, 225460, 490537, 1748155, 3167982, 9266618, 12543856, 12589961, 27359852, 3418801560, 8824909730, 72988555402

Offset: 1

Max Alekseyev, Dec 07 2013

The prime terms are given by A143853.

Cf. A065132, A143853, A233131.

s=0; pp=0; for(n=2,10^8, p=factor(n)[,1]; s += (n-2) - pp - sigma(n) +  sum(i=1,#p,p[i]) + if(!ispseudoprime(n),n,pp++;0) + 1; if(s%n==0,print1(n,", ")) )

cp's OEIS Frontend

A233131 Sum of remainders of n modulo all smaller composite numbers.

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