|
|
A338555
|
|
Numbers that are either a power of a prime or have relatively prime prime indices.
|
|
3
|
|
|
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 64, 66, 67, 68, 69, 70, 71, 72
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
Also Heinz numbers of partitions either constant or relatively prime (A338553). The Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), giving a bijective correspondence between positive integers and integer partitions.
|
|
LINKS
|
|
|
FORMULA
|
|
|
MATHEMATICA
|
Select[Range[100], #==1||PrimePowerQ[#]||GCD@@PrimePi/@First/@FactorInteger[#]==1&]
|
|
CROSSREFS
|
A327534 uses primes instead of prime powers.
A338553 counts the partitions with these Heinz numbers.
A000837 counts relatively prime partitions, with Heinz numbers A289509.
A018783 counts partitions whose prime indices are not relatively prime, with Heinz numbers A318978.
A051424 counts pairwise coprime or singleton partitions.
A327516 counts pairwise coprime partitions, with Heinz numbers A302696.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|