A065132 -id:A065132 - cp's OEIS frontend

A143851 Primes p that divide the sum of their residues modulo all smaller primes (=A024934(p)).

2, 13, 167, 2239, 439867, 724031017, 1990127567, 54892225873

Offset: 1

Neil Fernandez, Sep 03 2008

Also, primes p such that p divides A024924(p). The prime terms of A065132.

			13 is congruent to 1,1,3,6 and 2, modulo 2,3,5,7 and 11 respectively. 1+1+3+6+2=13, which is a multiple of the original number, 13. So the original number, is in the sequence.

Cf. A065132

For[n = 1, n < 1000001, n++, p = Prime[n]; m = Mod[Sum[Mod[p, Prime[i]], {i, 1, n - 1}], p]; If[m == 0, Print[p]]]

a(6)-a(8) from Max Alekseyev, Feb 10 2012

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

A143851 Primes p that divide the sum of their residues modulo all smaller primes (=A024934(p)).

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

Extensions