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A330946 Odd numbers whose prime indices are not all prime numbers. 7
7, 13, 19, 21, 23, 29, 35, 37, 39, 43, 47, 49, 53, 57, 61, 63, 65, 69, 71, 73, 77, 79, 87, 89, 91, 95, 97, 101, 103, 105, 107, 111, 113, 115, 117, 119, 129, 131, 133, 137, 139, 141, 143, 145, 147, 149, 151, 159, 161, 163, 167, 169, 171, 173, 175, 181, 183, 185 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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 MM-numbers of multiset partitions whose parts not all singletons (see example).
LINKS
EXAMPLE
The sequence of terms together with their prime indices of prime indices begins:
7: {{1,1}}
13: {{1,2}}
19: {{1,1,1}}
21: {{1},{1,1}}
23: {{2,2}}
29: {{1,3}}
35: {{2},{1,1}}
37: {{1,1,2}}
39: {{1},{1,2}}
43: {{1,4}}
47: {{2,3}}
49: {{1,1},{1,1}}
53: {{1,1,1,1}}
57: {{1},{1,1,1}}
61: {{1,2,2}}
63: {{1},{1},{1,1}}
65: {{2},{1,2}}
69: {{1},{2,2}}
71: {{1,1,3}}
73: {{2,4}}
MATHEMATICA
Select[Range[1, 100, 2], !And@@PrimeQ/@PrimePi/@First/@If[#==1, {}, FactorInteger[#]]&]
CROSSREFS
Odd numbers n such that A330944(n) > 0.
Including even numbers gives A330945.
The restriction to nonprimes is A330949.
Taking nonprimes instead of odds gives A330947.
The number of prime prime indices is given by A257994.
Primes of prime index are A006450.
Primes of nonprime index are A007821.
Products of primes of prime index are A076610.
Products of primes of nonprime index are A320628.
The set S of numbers whose prime indices do not all belong to S is A324694.
Sequence in context: A173928 A304995 A339657 * A160007 A024613 A024606
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 13 2020
STATUS
approved

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Last modified March 29 10:44 EDT 2024. Contains 371268 sequences. (Running on oeis4.)