A088948 Numbers k such that (A006530(k) + A020639(k))/2 is an integer; that is, arithmetic mean of least and largest prime factor is an integer.

2, 3, 4, 5, 7, 8, 9, 11, 13, 15, 16, 17, 19, 21, 23, 25, 27, 29, 31, 32, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 64, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125

Offset

1,1

Comments

Union of odd numbers and powers of 2 minus {1}. - Ivan Neretin, Dec 30 2015

In other words, the symmetric difference of sets A005408 (all prime factors are odd) and A000079 (all prime factors are even). If we had allowed 1 as a member, it would have been the union of A005408 and A000079, as stated. - Jeppe Stig Nielsen, Dec 27 2019

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Example

Primes and prime powers are here.
Also other composites: n=105, (3+7)/2 = 5 is an integer (and, moreover, divides n).

Mathematica

Rest@ Select[Range@ 125, IntegerQ[(FactorInteger[#][[1, 1]] + FactorInteger[#][[-1, 1]])/2] &] (* Michael De Vlieger, Mar 28 2015 *)
amintQ[n_]:=Module[{fi=FactorInteger[n][[;; , 1]]}, IntegerQ[Mean[{fi[[1]], fi[[-1]]}]]]; Select[Range[150], amintQ] (* Harvey P. Dale, Mar 02 2023 *)

Prog

(PARI) is_a088948(n) = {local (f); f=factor(n); if(Mod(vecmin(f[, 1])+vecmax(f[, 1]), 2)==0, 1, 0)} \\ Michael B. Porter, Mar 28 2015

Crossrefs

Different from A046687.

Cf. A006530, A020639, A088949, A088949, A046687.

Sequence in context: A078174 A174894 A275616 * A369096 A115405 A343857

Adjacent sequences: A088945 A088946 A088947 * A088949 A088950 A088951

Keyword

nonn

Author

Labos Elemer, Nov 20 2003

Status

approved