A327902 Nonprime squarefree numbers whose prime indices all have the same average of prime indices (A326567/A326568).

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

Offset: 1

Author

Gus Wiseman, Sep 30 2019

Keywords

• nonn

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.

Examples

			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}
		

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.

Programs

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[#]&];