A327901 Nonprime squarefree numbers whose prime indices all have the same sum of prime indices (A056239).

1, 35, 143, 209, 247, 391, 493, 629, 667, 851, 901, 1073, 1219, 1333, 1457, 1537, 1891, 1961, 2021, 2201, 2623, 2717, 2759, 2867, 2993, 3053, 3239, 3337, 3827, 3977, 4061, 4183, 4223, 4331, 4387, 4633, 5429, 5633, 5767, 5959, 6157, 6191, 6319, 7081, 7093, 7519

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..46.

Gus Wiseman, Sequences counting and ranking multiset partitions whose part lengths, sums, or averages are constant or strict.

Example

The sequence of terms together with their prime indices begins:
     1: {}
    35: {3,4}
   143: {5,6}
   209: {5,8}
   247: {6,8}
   391: {7,9}
   493: {7,10}
   629: {7,12}
   667: {9,10}
   851: {9,12}
   901: {7,16}
  1073: {10,12}
  1219: {9,16}
  1333: {11,14}
  1457: {11,15}
  1537: {10,16}
  1891: {11,18}
  1961: {12,16}
  2021: {14,15}
  2201: {11,20}

Mathematica

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[1000], !PrimeQ[#]&&SquareFreeQ[#]&&SameQ@@Total/@primeMS/@primeMS[#]&];

Crossrefs

The version including primes and nonsquarefree numbers is A326534.

The version for number of prime indices is A327900.

The version for mean of prime indices is A327902.

Cf. A001222, A005117, A056239, A112798, A302242, A306021, A320324, A326566, A326574, A327908.

Sequence in context: A157286 A354543 A324072 * A346910 A290560 A136017

Adjacent sequences: A327898 A327899 A327900 * A327902 A327903 A327904

Keyword

nonn

Author

Gus Wiseman, Sep 30 2019

Status

approved