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A330947 Nonprime numbers whose prime indices are all prime numbers. 7
1, 9, 15, 25, 27, 33, 45, 51, 55, 75, 81, 85, 93, 99, 121, 123, 125, 135, 153, 155, 165, 177, 187, 201, 205, 225, 243, 249, 255, 275, 279, 289, 295, 297, 327, 335, 341, 363, 369, 375, 381, 405, 415, 425, 451, 459, 465, 471, 495, 527, 531, 537, 545, 561, 573 (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.

LINKS

Table of n, a(n) for n=1..55.

EXAMPLE

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

    1: {}

    9: {{1},{1}}

   15: {{1},{2}}

   25: {{2},{2}}

   27: {{1},{1},{1}}

   33: {{1},{3}}

   45: {{1},{1},{2}}

   51: {{1},{4}}

   55: {{2},{3}}

   75: {{1},{2},{2}}

   81: {{1},{1},{1},{1}}

   85: {{2},{4}}

   93: {{1},{5}}

   99: {{1},{1},{3}}

  121: {{3},{3}}

  123: {{1},{6}}

  125: {{2},{2},{2}}

  135: {{1},{1},{1},{2}}

  153: {{1},{1},{4}}

  155: {{2},{5}}

MATHEMATICA

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

CROSSREFS

Complement in A076610 of A000040.

Complement in A018252 of A330948.

Nonprime numbers n such that A330944(n) = 0.

Taking odds instead of nonprimes gives A330946.

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.

Numbers whose prime indices are not all prime are A330945.

Cf. A000720, A001222, A056239, A112798, A302242, A320629, A320633, A330949.

Sequence in context: A145743 A164384 A138193 * A337237 A036315 A340120

Adjacent sequences:  A330944 A330945 A330946 * A330948 A330949 A330950

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 13 2020

STATUS

approved

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Last modified September 16 07:10 EDT 2021. Contains 347469 sequences. (Running on oeis4.)