A326158 Nonprime squarefree numbers whose product of prime indices is divisible by their sum of prime indices.

30, 65, 154, 165, 190, 259, 273, 385, 390, 435, 442, 481, 506, 561, 595, 609, 658, 714, 741, 781, 874, 935, 1001, 1110, 1118, 1173, 1254, 1281, 1330, 1363, 1403, 1430, 1455, 1469, 1495, 1505, 1653, 1691, 1771, 1786, 1794, 1798, 1887, 1958, 2035, 2067, 2139

Offset

1,1

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

The sequence of terms together with their prime indices begins:
    30: {1,2,3}
    65: {3,6}
   154: {1,4,5}
   165: {2,3,5}
   190: {1,3,8}
   259: {4,12}
   273: {2,4,6}
   385: {3,4,5}
   390: {1,2,3,6}
   435: {2,3,10}
   442: {1,6,7}
   481: {6,12}
   506: {1,5,9}
   561: {2,5,7}
   595: {3,4,7}
   609: {2,4,10}
   658: {1,4,15}
   714: {1,2,4,7}
   741: {2,6,8}
   781: {5,20}

Mathematica

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[2, 1000], !PrimeQ[#]&&SquareFreeQ[#]&&Divisible[Times@@primeMS[#], Plus@@primeMS[#]]&]

Crossrefs

Satisfies A056239(a(n))|A003963(a(n)).

The case with squarefree numbers included is A326150.

The case with primes and squarefree numbers included is A326149.

Cf. A057567, A057568, A112798, A301987.

Cf. A325037, A325042, A325044, A326151, A326153/A326154, A326155, A326156.

Sequence in context: A042798 A320705 A132771 * A300790 A175259 A044132

Adjacent sequences: A326155 A326156 A326157 * A326159 A326160 A326161

Keyword

nonn

Author

Gus Wiseman, Jun 10 2019

Status

approved