|
|
A348520
|
|
Pentaphobe or 5-phobe numbers: integers that are not pentaphile numbers.
|
|
4
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn,fini,full
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|