A225720 - OEIS

%I #13 Nov 05 2017 00:41:57

%S 10,79222,206965,784090,1673122,2227123,4798090,5202571,9196330,

%T 13146715,15015430,18213595,19342333,21735010,27907435,28234018,

%U 28240090,37394146,38710990,53990695,54772453,70646509,79671826,89678830,107251990,114572545,115005187,137245690

%N Composite squarefree numbers n such that p+10 divides n-10 for each prime p dividing n.

%e Prime factors of 2227123 are 19, 251 and 467. We have that (2227123-10)/(19+10) = 76797, (2227123-10)/(251+10) = 8533 and (2227123-10)/(467+10) = 4669.

%p with(numtheory); A225720:=proc(i,j) local c, d, n, ok, p, t;

%p for n from 2 to i do if not isprime(n) then p:=ifactors(n)[2]; ok:=1;

%p for d from 1 to nops(p) do if p[d][2]>1 or p[d][1]=j then ok:=0; break; fi;

%p if  not type((n+j)/(p[d][1]-j),integer) then ok:=0; break; fi; od;

%p if ok=1 then print(n); fi; fi; od; end: A225720(10^9,-10);

%o (PARI) is(n,f=factor(n))=if(#f[,2]<2 || vecmax(f[,2])>1, return(0)); for(i=1,#f~, if((n-10)%(f[i,1]+10), return(0))); 1 \\ _Charles R Greathouse IV_, Nov 05 2017

%Y Cf. A208728, A225702-A225719.

%K nonn

%O 1,1

%A _Paolo P. Lava_, May 13 2013

%E a(20)-a(27) from _Donovan Johnson_, Nov 15 2013

%E a(28) from _Charles R Greathouse IV_, Nov 05 2017