A335580 - OEIS

%I #16 Feb 01 2021 13:31:22

%S 3,6,14,38,61,164,248,402,677,1808,11518,21018,54436,76926,109950,

%T 461745,601650,792962,1183573,8198625

%N Numbers k such that A335579(k) is divisible by at least one of the composites between prime(k) and prime(k+1).

%e a(3) = 14 is in the sequence because A335579(14) = 230 is divisible by 46, which is between prime(14) = 43 and prime(15) = 47.

%p filter:= proc(n) local i,S,s;

%p     S:= `union`(seq(numtheory:-divisors(i),i=ithprime(n)+1..ithprime(n+1)-1));

%p     s:= convert(S,`+`);

%p     for i from ithprime(n)+1 to ithprime(n+1)-1 do

%p       if s mod i = 0 then return true fi

%p     od;

%p     false

%p end proc:

%p select(filter, [$1..10^5]);

%o (PARI) f(n) = my(s=[]); for (c=prime(n)+1, prime(n+1)-1, s = setunion(s, divisors(c))); vecsum(s); \\ A335579

%o isok(k) = my(s=f(k)); for (c=prime(k)+1, prime(k+1)-1, if (!(s % c), return (1))); \\ _Michel Marcus_, Feb 01 2021

%Y Cf. A335579.

%K nonn,more

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Jan 26 2021