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

1,2

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.

Links

Table of n, a(n) for n=1..23.

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

Example

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.

Mathematica

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

Prog

(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

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).

Sequence in context: A303550 A164563 A179892 * A061773 A125007 A290748

Adjacent sequences: A348516 A348517 A348518 * A348520 A348521 A348522

Keyword

nonn,fini,full

Author

Bernard Schott, Oct 23 2021

Status

approved