A363681 Sphenic numbers sandwiched between two squarefree semiprimes.

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.

Links

Table of n, a(n) for n=1..52.

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

Cf. A006881, A007304, A362811

Sequence in context: A124207 A189941 A362811 * A260923 A151701 A258276

Adjacent sequences: A363678 A363679 A363680 * A363682 A363683 A363684

Keyword

nonn

Author

Tanya Khovanova and Massimo Kofler, Jun 14 2023

Status

approved