A348519 Tetraphobe or 4-phobe numbers: integers that are not tetraphile numbers.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 20, 24, 25, 26, 32, 48

Offset: 1

Author

Bernard Schott, Oct 23 2021

Keywords

• nonn
• fini
• full

Comments

Tetraphile numbers are described in A348517.

The idea for this sequence comes from the French website Diophante (see link).

It is possible to generalize for "k-phile" or "k-phobe" numbers (see Crossrefs).

The set of k-phobe numbers is always finite, the smallest one is always 1; here, there exist 23 tetraphobe numbers and the largest one is 48.

Examples

			There are no 4 positive integers b_1 < b_2 < b_3 < b_4 such that b_1 divides b_2, b_2 divides b_3, b_3 divides b_4, and 17 = b_1 + b_2 + b_3 + b_4, hence 17 is a term.
		

Links

• Diophante, A496 - Pentaphiles et pentaphobes (in French).

Crossrefs

k-phile numbers: A160811 \ {5} (k=3), A348517 (k=4), A348518 (k=5).

k-phobe numbers: A019532 (k=3), this sequence (k=4), A348520 (k=5).

Programs

Mathematica

Select[Range@48,Select[Select[IntegerPartitions[#,{4}],Length@Union@#==4&],And@@(IntegerQ/@Divide@@@Partition[#,2,1])&]=={}&] (* Giorgos Kalogeropoulos, Oct 24 2021 *)

PARI

isok(k) = forpart(p=k, if (#Set(p) == 4, if (!(p[2] % p[1]) && !(p[3] % p[2]) && !(p[4] % p[3]), return(0))), , [4, 4]); return(1); \\ Michel Marcus, Nov 14 2021