A336028 The least k such that i*k + 1 is a product of i (not necessarily distinct) primes for i = 1, ..., n.

1, 4, 108, 3306, 7576, 14502646, 6247706232

Offset

1,2

Links

Table of n, a(n) for n=1..7.

Vladimir Letsko, Problem K7 (in Russian).

Example

108 is in the sequence because 108 + 1 is prime, 2*108 + 1 is a product of 2 primes (7, 31), 3*108 + 1 is a product of 3 primes (5, 5, 13), and 108 is the least number with such properties.

Maple

for kk to 6 do n := 1;
do n := nextprime(n); f := true;
for k from 2 to kk do a := ifactors(k*(n-1)+1)[2]; b := add(c[2], c in a);
if b <> k then f := false; break end if end do; if f then print(n-1); break end if end do end do

Prog

(PARI) is(k, n) = for(i=1, n, if(bigomega(i*k+1)!=i, return(1)));
a(n) = for(k=1, oo, if(!is(k, n), return(k))); \\ Jinyuan Wang, Jul 08 2020

Crossrefs

Cf. A000005, A001222, A336027.

Sequence in context: A269270 A302113 A357510 * A131092 A360092 A123056

Adjacent sequences: A336025 A336026 A336027 * A336029 A336030 A336031

Keyword

nonn,more

Author

Vladimir Letsko, Jul 05 2020

Status

approved