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A326158 Nonprime squarefree numbers whose product of prime indices is divisible by their sum of prime indices. 11
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 (list; graph; refs; listen; history; text; internal format)
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
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.
Sequence in context: A042798 A320705 A132771 * A300790 A175259 A044132
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 10 2019
STATUS
approved

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Last modified July 15 14:40 EDT 2024. Contains 374332 sequences. (Running on oeis4.)