

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
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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 MMnumbers 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 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.
Cf. A000040, A000720, A001222, A018252, A056239, A112798, A302242, A320629, A330943, A330947, A330948.


KEYWORD

nonn


AUTHOR



STATUS

approved



