A361363 Primitive terms of A259850.

1, 3, 8, 14, 15, 21, 26, 40, 130, 144, 182, 255, 310, 372, 465, 468, 680, 980, 1524, 2170, 2210, 2418, 2448, 4030, 4536, 7008, 7956, 8890, 9906, 10220, 10416, 10668, 12648, 16335, 16660, 17082, 20216, 24624, 30800, 36792, 41106, 44055, 48400, 65535, 77112, 78320, 85120, 97790, 143000, 149688

Offset: 1

Author

Robert Israel, Mar 09 2023

Keywords

• nonn

Comments

Terms k of A259850 such that no earlier term of A259850 has the same set of prime factors as k.

Numbers k such that k/phi(k) = sigma(x)/x for some x<=k, and there do not exist m and y with y <= m < k such that m has the same set of prime factors as k and sigma(y)/y = k/phi(k).

Examples

			a(4) = 14 is a term because 14 = A259850(5) is the first term of A259850 whose set of prime factors is {2,7}.
28 = A259850(11) is not a term because it has the same set {2,7} of prime factors as 14.
		

Crossrefs

Cf. A000010, A000203, A259850.

Programs

Maple

R:= NULL: count:= 0: V:= {}: S:= {}:
for k from 1 while count < 50 do
 V:= V union  {numtheory:-sigma(k)/k};
 if member(k/numtheory:-phi(k), V) then
   s:= numtheory:-factorset(k);
     if not member(s,S) then
      R:= R, k; count:= count+1; S:= S union {s}
   fi fi;
od:
R;