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A327902 Nonprime squarefree numbers whose prime indices all have the same average of prime indices (A326567/A326568). 3
1, 21, 57, 115, 133, 145, 159, 371, 393, 399, 515, 535, 565, 667, 803, 869, 917, 933, 1007, 1067, 1113, 1963, 2021, 2095, 2157, 2165, 2177, 2249, 2285, 2315, 2363, 2369, 2461, 2489, 2599, 2705, 2751, 2839, 2987, 3021, 3103, 3277, 3335, 3707, 3859, 4331, 4367 (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..47.

EXAMPLE

The sequence of terms together with their prime indices begins:

     1: {}

    21: {2,4}

    57: {2,8}

   115: {3,9}

   133: {4,8}

   145: {3,10}

   159: {2,16}

   371: {4,16}

   393: {2,32}

   399: {2,4,8}

   515: {3,27}

   535: {3,28}

   565: {3,30}

   667: {9,10}

   803: {5,21}

   869: {5,22}

   917: {4,32}

   933: {2,64}

  1007: {8,16}

  1067: {5,25}

MATHEMATICA

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];

Select[Range[1000], !PrimeQ[#]&&SquareFreeQ[#]&&SameQ@@Mean/@primeMS/@primeMS[#]&];

CROSSREFS

The version including primes and nonsquarefree numbers is A326536.

The version for number of prime indices is A327900.

The version for sum of prime indices is A327901.

Cf. A001222, A005117, A056239, A078175, A102627, A112798, A316413, A326567/A326568, A326621, A327908.

Sequence in context: A044123 A044504 A118057 * A020148 A037305 A223467

Adjacent sequences:  A327899 A327900 A327901 * A327903 A327904 A327905

KEYWORD

nonn

AUTHOR

Gus Wiseman, Sep 30 2019

STATUS

approved

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Last modified May 19 18:35 EDT 2022. Contains 353847 sequences. (Running on oeis4.)