A335580 Numbers k such that A335579(k) is divisible by at least one of the composites between prime(k) and prime(k+1).

3, 6, 14, 38, 61, 164, 248, 402, 677, 1808, 11518, 21018, 54436, 76926, 109950, 461745, 601650, 792962, 1183573, 8198625

Offset

1,1

Links

Table of n, a(n) for n=1..20.

Example

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.

Maple

filter:= proc(n) local i, S, s;
    S:= `union`(seq(numtheory:-divisors(i), i=ithprime(n)+1..ithprime(n+1)-1));
    s:= convert(S, `+`);
    for i from ithprime(n)+1 to ithprime(n+1)-1 do
      if s mod i = 0 then return true fi
    od;
    false
end proc:
select(filter, [$1..10^5]);

Prog

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

Crossrefs

Cf. A335579.

Sequence in context: A106395 A369544 A261436 * A079003 A099966 A101162

Adjacent sequences: A335577 A335578 A335579 * A335581 A335582 A335583

Keyword

nonn,more

Author

J. M. Bergot and Robert Israel, Jan 26 2021

Status

approved