A029553 Quasi-Carmichael numbers to base 10: squarefree composites n such that (n,2*3*5*7) = 1 and prime p|n ==> p-10|n-10.

4807, 46189, 290719, 423181, 753763, 1188847, 3863233, 8457823, 8810413, 15058963, 16948789, 23524489, 33402841, 37912087, 40018303, 41874661, 43401511, 58953817, 62012989, 73792981, 75598687, 89269333, 107492437, 140757067

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

If multiples of 2, 3, 5 and 7 are not excluded, then terms like 10, 55, 66, 91, 130, 154,... belong to the sequence. - Giovanni Resta, May 21 2013

Links

• Giovanni Resta, Table of n, a(n) for n = 1..268 (terms < 10^12)
• Index entries for sequences related to Carmichael numbers.

Programs

Mathematica

qcm[n_, d_] := Block[{p, e}, {p, e} = Transpose@FactorInteger@n; Length[p] > 1 && Max[e] == 1 && d < Min[p] && And @@ IntegerQ /@ ((n - d)/(p - d))]; Select[Range[10^6], qcm[#, 10] &] (* Giovanni Resta, May 21 2013 *)