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A361908
Positive integers > 1 whose prime indices satisfy (maximum) = 2*(minimum).
11
6, 12, 18, 21, 24, 36, 48, 54, 63, 65, 72, 96, 105, 108, 133, 144, 147, 162, 189, 192, 216, 288, 315, 319, 324, 325, 384, 432, 441, 455, 481, 486, 525, 567, 576, 648, 715, 731, 735, 768, 845, 864, 931, 945, 972, 1007, 1029, 1152, 1296, 1323, 1403, 1458, 1463
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.
EXAMPLE
The terms together with their prime indices begin:
6: {1,2}
12: {1,1,2}
18: {1,2,2}
21: {2,4}
24: {1,1,1,2}
36: {1,1,2,2}
48: {1,1,1,1,2}
54: {1,2,2,2}
63: {2,2,4}
65: {3,6}
72: {1,1,1,2,2}
96: {1,1,1,1,1,2}
MATHEMATICA
Select[Range[2, 100], PrimePi[FactorInteger[#][[-1, 1]]]==2*PrimePi[FactorInteger[#][[1, 1]]]&]
CROSSREFS
The RHS is 2*A055396 (twice minimum).
The LHS is A061395 (greatest prime index).
Partitions of this type are counted by A118096.
For mean instead of minimum we have A361855, counted by A361853.
For median instead of minimum we have A361856, counted by A361849.
For length instead of minimum we have A361909, counted by A237753.
A001221 (omega) counts distinct prime factors.
A001222 (bigomega) counts prime factors with multiplicity.
A112798 lists prime indices, sum A056239.
Sequence in context: A364537 A350845 A315723 * A160594 A315724 A146538
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 05 2023
STATUS
approved