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A363681
Sphenic numbers sandwiched between two squarefree semiprimes.
0
186, 266, 322, 470, 518, 534, 582, 590, 670, 754, 790, 814, 894, 994, 1146, 1158, 1166, 1338, 1390, 1562, 1686, 1798, 1842, 1958, 2118, 2158, 2230, 2318, 2454, 2482, 2514, 2570, 2630, 2758, 2786, 2922, 2930, 2994, 3154, 3206, 3262, 3278, 3378, 3454, 3522, 3562, 3714, 3786, 3830, 3838, 3962, 3982
OFFSET
1,1
COMMENTS
Sphenic numbers are numbers that are products of three distinct primes.
This sequence is different from A362811: sphenic numbers sandwiched between semiprimes, as semiprimes are products of two primes that might not be distinct.
EXAMPLE
186 = 2*3*31 is a sphenic number sandwiched between 185 = 5*37 and 187 = 11*17, both of which are squarefree semiprimes. Thus, 186 is in this sequence.
290 = 2*5*29 is a sphenic number sandwiched between semiprimes 289 = 17*17 and 291 = 3*97, one of which is not squarefree. Thus, 290 is not in this sequence but in A362811.
MATHEMATICA
Select[Range[4000], Transpose[FactorInteger[#]][[2]] == {1, 1, 1} && Transpose[FactorInteger[# - 1]][[2]] == {1, 1} && Transpose[FactorInteger[# + 1]][[2]] == {1, 1} &]
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved