A225719 -id:A225719 - cp's OEIS frontend

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

Paolo P. Lava, May 13 2013

nonn

			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.

Cf. A208728, A225702-A225719.

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);

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

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

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

A225718 Composite squarefree numbers n such that p(i)+8 divides n-8, where p(i) are the prime factors of n.

Original entry on oeis.org

4958, 51653, 55583, 271358, 291338, 789173, 1379438, 5430797, 5785073, 6350885, 7159958, 10532333, 12822818, 13892243, 14809517, 23831423, 24547058, 26734058, 27391073, 32079671, 32673383, 36126098, 42560693, 51346358, 52177658, 54949958

Offset: 1

Paolo P. Lava, May 13 2013

nonn

			Prime factors of 789173 are 7, 11, 37 and 277. We have that (789173-8)/(7+8) = 52611, (789173-8)/(11+8) = 41535, (789173-8)/(37+8) = 17537 and (789173-8)/(277+8) = 2769.

Cf. A208728, A225702-A225717, A225719, A225720.

with(numtheory); A225718:=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: A225718(10^9,-8);

cp's OEIS Frontend

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

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