login
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
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.
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.
Sequence in context: A044123 A044504 A118057 * A020148 A370519 A037305
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 30 2019
STATUS
approved