A088948 -id:A088948 - cp's OEIS frontend

A088595 Numbers n such that (A006530(n) + A020639(n))/2 is an integer, divides n and it is not a power of prime number: it has at least 2 distinct prime factors. Special terms of A088948.

105, 231, 315, 525, 627, 693, 735, 897, 935, 945, 1155, 1575, 1581, 1617, 1729, 1881, 2079, 2205, 2465, 2541, 2625, 2691, 2835, 2967, 3135, 3465, 3525, 3675, 4123, 4301, 4389, 4485, 4675, 4715, 4725, 4743, 4851, 5145, 5487, 5643, 5775, 6237, 6279, 6545

Offset: 1

Labos Elemer, Nov 20 2003

nonn

Every number of the sequence has at least three different prime factors. Also, the sequence is infinite (it contains all numbers of the form 3^a*5^b*7^c with a,b,c>0). - Emmanuel Vantieghem, Nov 21 2016

			n = 315 = 3*3*5*7 is not a power of a prime, has 3 prime factors and (3+5)/2=7 divides n.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A006530, A020639, A088948, A088949.

filter:= proc(n) local F;
  F:= numtheory:-factorset(n);
  nops(F) > 2 and n mod (min(F)+max(F))/2 = 0
end proc:
select(filter, [seq(i,i=1..10^4,2)]); # Robert Israel, Nov 21 2016

Rest@ Select[Range@ 6600, Function[n, And[IntegerQ@ #, Divisible[n, #], ! PrimePowerQ@ n] &[(#[[-1, 1]] + #[[1, 1]])/2] &@ FactorInteger@ n]] (* Michael De Vlieger, Nov 24 2016 *)

A088949 Composite numbers k such that (A006530(k) + A020639(k))/2 is an integer that divides k; special terms of A088948.

Original entry on oeis.org

4, 8, 9, 16, 25, 27, 32, 49, 64, 81, 105, 121, 125, 128, 169, 231, 243, 256, 289, 315, 343, 361, 512, 525, 529, 625, 627, 693, 729, 735, 841, 897, 935, 945, 961, 1024, 1155, 1331, 1369, 1575, 1581, 1617, 1681, 1729, 1849, 1881, 2048, 2079, 2187, 2197, 2205, 2209

Offset: 1

Labos Elemer, Nov 20 2003

nonn

			k = 315 = 3*3*5*7 (composite); (3 + 7)/2 = 5, which divides k.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A006530, A020639, A088948, A088595, A046687.

q[k_] := CompositeQ[k] && Module[{p = FactorInteger[k][[;;, 1]], m}, m = (p[[1]] + p[[-1]]); EvenQ[m] && Divisible[k, m/2]]; Select[Range[2500], q] (* Amiram Eldar, Mar 01 2025 *)

lista(nn) = {forcomposite(n=1, nn, my(f = factor(n)[,1], x = (vecmin(f) + vecmax(f))/2); if ((denominator(x)==1) && !(n % x), print1(n, ", ")););} \\ Michel Marcus, Jul 09 2018

Edited by Jon E. Schoenfield, Jul 08 2018

More terms from Michel Marcus, Jul 09 2018

cp's OEIS Frontend

A088595 Numbers n such that (A006530(n) + A020639(n))/2 is an integer, divides n and it is not a power of prime number: it has at least 2 distinct prime factors. Special terms of A088948.

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