OFFSET
1,1
COMMENTS
Subsequence of A309769. Even number m is a term if and only if for every odd prime divisor p, m can be written as 2*r*p, where r >= 2, and p is greater than the smallest prime divisor of 2*r-1.
From above, 4^k*p is a term for every prime p >= 5 and k >= 1. - David A. Corneth, Aug 17 2019
More general than the above, David James Sycamore finds (2*r)^k * p is a term for all r>=2, k>=1 and prime p > q, the smallest prime divisor of 2*r-1. - David A. Corneth, Aug 26 2019
EXAMPLE
20 = 4*5 is a term (k=2 for p=5).
110 = 10*11 = 22*5 is a term (k=8 for p=11 and k=2 for p=5).
MATHEMATICA
kQ[n_, p_] := Module[{ans = False}, Do[If[Divisible[n - k, p - k], ans = True; Break[]], {k, 1, p - 2}]; ans]; aQ[n_] := EvenQ[n] && Length[(p = FactorInteger[ n][[2 ;; -1, 1]])] > 0 && AllTrue[p, kQ[n, #] &]; Select[Range[500], aQ] (* Amiram Eldar, Aug 17 2019 *)
PROG
(PARI) getk(p, m) = {for (k=1, p-2, if (((m-k) % (p-k)) == 0, return(k)); ); }
isok(m) = {if ((m % 2) == 0, my(f = factor(m)[, 1]~); if (#f == 1, return (0)); for (i=2, #f, if (!getk(f[i], m), return(0)); ); return (1); ); } \\ Michel Marcus, Aug 26 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
David James Sycamore, Aug 17 2019
EXTENSIONS
More terms from Amiram Eldar, Aug 17 2019
STATUS
approved