A225720 Composite squarefree numbers n such that p+10 divides n-10 for each prime p dividing n.

10, 79222, 206965, 784090, 1673122, 2227123, 4798090, 5202571, 9196330, 13146715, 15015430, 18213595, 19342333, 21735010, 27907435, 28234018, 28240090, 37394146, 38710990, 53990695, 54772453, 70646509, 79671826, 89678830, 107251990, 114572545, 115005187, 137245690

Offset: 1

Author

Paolo P. Lava, May 13 2013

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A208728, A225702-A225719.

Programs

Maple

with(numtheory); A225720:=proc(i,j) local c, d, n, ok, p, t;
for n from 2 to i do if not isprime(n) then p:=ifactors(n)[2]; ok:=1;
for d from 1 to nops(p) do if p[d][2]>1 or p[d][1]=j then ok:=0; break; fi;
if  not type((n+j)/(p[d][1]-j),integer) then ok:=0; break; fi; od;
if ok=1 then print(n); fi; fi; od; end: A225720(10^9,-10);

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

Extensions

a(20)-a(27) from Donovan Johnson, Nov 15 2013

a(28) from Charles R Greathouse IV, Nov 05 2017