A348520 Pentaphobe or 5-phobe numbers: integers that are not pentaphile numbers.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 44, 48, 49, 50, 51, 52, 53, 54, 56, 60, 65, 66, 68, 72, 74, 80, 84, 97, 98, 102, 104, 108, 120, 132, 144, 168, 194, 240

Offset

1,2

Comments

Pentaphile numbers are described in A348518.

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 and the smallest one is always 1; here, there exist 68 pentaphobe numbers and the largest one is 240.

Links

Table of n, a(n) for n=1..68.

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

Example

There are no 5 positive integers b_1 < b_2 < b_3 < b_4 < b_5 such that b_1 divides b_2, b_2 divides b_3, b_3 divides b_4, b_4 divides b_5, and 32 = b_1 + b_2 + b_3 + b_4 + b_5, hence 32 is a term.

Prog

(PARI) isok(k) = forpart(p=k, if (#Set(p) == 5, if (!(p[2] % p[1]) && !(p[3] % p[2]) && !(p[4] % p[3]) && !(p[5] % p[4]), return(0))), , [5, 5]); 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), A348519 (k=4), this sequence (k=5).

Sequence in context: A123068 A247064 A160547 * A230034 A269331 A246103

Adjacent sequences: A348517 A348518 A348519 * A348521 A348522 A348523

Keyword

nonn,fini,full

Author

Bernard Schott, Nov 02 2021

Status

approved