A330945 - OEIS

A330945

Numbers whose prime indices are not all prime numbers.

2, 4, 6, 7, 8, 10, 12, 13, 14, 16, 18, 19, 20, 21, 22, 23, 24, 26, 28, 29, 30, 32, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 46, 47, 48, 49, 50, 52, 53, 54, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 82, 84, 86, 87

(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.

LINKS

Table of n, a(n) for n=1..66.

EXAMPLE

The sequence of terms together with their prime indices of prime indices begins:

2: {{}}

4: {{},{}}

6: {{},{1}}

7: {{1,1}}

8: {{},{},{}}

10: {{},{2}}

12: {{},{},{1}}

13: {{1,2}}

14: {{},{1,1}}

16: {{},{},{},{}}

18: {{},{1},{1}}

19: {{1,1,1}}

20: {{},{},{2}}

21: {{1},{1,1}}

22: {{},{3}}

23: {{2,2}}

24: {{},{},{},{1}}

26: {{},{1,2}}

28: {{},{},{1,1}}

29: {{1,3}}

MATHEMATICA

Select[Range[100], !And@@PrimeQ/@PrimePi/@First/@If[#==1, {}, FactorInteger[#]]&]

CROSSREFS

Complement of A076610 (products of primes of prime index).

Numbers n such that A330944(n) > 0.

The restriction to odd terms is A330946.

The restriction to nonprimes is A330948.

The number of prime prime indices is given by A257994.

The number of nonprime prime indices is given by A330944.

Primes of prime index are A006450.

Primes of nonprime index are A007821.

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, A320633, A330943, A330947, A330949.

Sequence in context: A080645 A024413 A153347 * A153167 A227187 A047237

Adjacent sequences: A330942 A330943 A330944 * A330946 A330947 A330948

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 13 2020

STATUS

approved