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A326150 Nonprime numbers whose product of prime indices is divisible by their sum of prime indices. 7
9, 30, 49, 63, 65, 81, 84, 108, 125, 150, 154, 165, 169, 190, 198, 200, 259, 264, 273, 333, 351, 361, 364, 385, 390, 435, 442, 468, 481, 490, 495, 506, 525, 561, 580, 595, 609, 624, 630, 658, 675, 700, 714, 741, 765, 781, 783, 810, 840, 841, 846, 874, 900, 918 (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:
9: {2,2}
30: {1,2,3}
49: {4,4}
63: {2,2,4}
65: {3,6}
81: {2,2,2,2}
84: {1,1,2,4}
108: {1,1,2,2,2}
125: {3,3,3}
150: {1,2,3,3}
154: {1,4,5}
165: {2,3,5}
169: {6,6}
190: {1,3,8}
198: {1,2,2,5}
200: {1,1,1,3,3}
259: {4,12}
264: {1,1,1,2,5}
273: {2,4,6}
333: {2,2,12}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[2, 1000], !PrimeQ[#]&&Divisible[Times@@primeMS[#], Plus@@primeMS[#]]&]
CROSSREFS
Satisfies A056239(a(n))|A003963(a(n)).
The case with primes included is A326149. The squarefree case A326158.
Sequence in context: A158503 A179506 A185653 * A167154 A063150 A063161
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 09 2019
STATUS
approved

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Last modified May 25 04:52 EDT 2024. Contains 372782 sequences. (Running on oeis4.)