|
| |
|
|
A329630
|
|
Products of distinct primes of nonprime squarefree index.
|
|
2
|
|
|
|
1, 2, 13, 26, 29, 43, 47, 58, 73, 79, 86, 94, 101, 113, 137, 139, 146, 149, 158, 163, 167, 181, 199, 202, 226, 233, 257, 269, 271, 274, 278, 293, 298, 313, 317, 326, 334, 347, 349, 362, 373, 377, 389, 397, 398, 421, 439, 443, 449, 466, 467, 487, 491, 499, 514
(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. The multiset of multisets with MM-number n is formed by taking the multiset of prime indices of each part of the multiset of prime indices of n. For example, the prime indices of 78 are {1,2,6}, so the multiset of multisets with MM-number 78 is {{},{1},{1,2}}. This sequence lists all MM-numbers of sets of non-singleton sets.
|
|
|
LINKS
|
Table of n, a(n) for n=1..55.
|
|
|
EXAMPLE
|
The sequence of terms together with their corresponding sets of sets begins:
1: {}
2: {{}}
13: {{1,2}}
26: {{},{1,2}}
29: {{1,3}}
43: {{1,4}}
47: {{2,3}}
58: {{},{1,3}}
73: {{2,4}}
79: {{1,5}}
86: {{},{1,4}}
94: {{},{2,3}}
101: {{1,6}}
113: {{1,2,3}}
137: {{2,5}}
139: {{1,7}}
146: {{},{2,4}}
149: {{3,4}}
158: {{},{1,5}}
163: {{1,8}}
|
|
|
MATHEMATICA
|
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], SquareFreeQ[#]&&And@@SquareFreeQ/@primeMS[#]&&!MemberQ[primeMS[#], _?PrimeQ]&]
|
|
|
CROSSREFS
|
MM-numbers of sets of nonempty sets are A329629.
Products of primes of nonprime squarefree index are A320630.
Products of prime numbers of squarefree index are A302478.
Products of primes of nonprime index are A320628.
Cf. A005117, A056239, A112798, A302242, A302494, A329557.
Classes of MM-numbers: A305078 (connected), A316476 (antichains), A318991 (chains), A320456 (covers), A329559 (clutters).
Sequence in context: A297955 A298578 A299570 * A018628 A018657 A161711
Adjacent sequences: A329627 A329628 A329629 * A329631 A329632 A329633
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Gus Wiseman, Nov 18 2019
|
|
|
STATUS
|
approved
|
| |
|
|
