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 A358686 Numbers sandwiched between two semiprimes, one of which is a square. 1
 5, 50, 120, 122, 288, 290, 528, 842, 960, 1370, 1680, 1850, 2808, 2810, 4488, 5328, 5330, 6240, 6242, 6888, 6890, 9408, 9410, 11880, 12768, 18770, 22200, 22800, 26568, 27888, 36482, 38808, 39600, 52440, 54290, 58080, 63000, 63002, 69170, 72360, 72362, 73442, 76730, 78960 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers in A124936 but not in A358665. All numbers except 5 (the first term) are even. Subsequence of A124936. LINKS Harvey P. Dale, Table of n, a(n) for n = 1..292 (all terms up to 10 million) EXAMPLE 5 is sandwiched between two semiprimes 4 = 2*2 and 6 = 3*2, one of which is a square. Thus, 5 is in this sequence. 34 is sandwiched between squarefree semiprimes 33 = 3*11 and 35 = 5*7. Thus, 34 is not in this sequence. MATHEMATICA Select[Range[100000], Total[Transpose[FactorInteger[# - 1]][[2]]] == 2 && Total[Transpose[FactorInteger[# + 1]][[2]]] == 2 && ! (Transpose[FactorInteger[# - 1]][[2]] == {1, 1} && Transpose[FactorInteger[# + 1]][[2]] == {1, 1}) &] Mean/@Select[SequencePosition[PrimeOmega[Range[80000]], {2, _, 2}], AnyTrue[Sqrt[#], IntegerQ]&] (* Harvey P. Dale, Jun 14 2023 *) PROG (Python) from sympy import factorint from itertools import count, islice def agen(): # generator of terms nxt = [] yield 5 for k in count(6, 2): prv, nxt = nxt, list(factorint(k+1).values()) if (prv==[1, 1] and nxt==[2]) or (prv==[2] and nxt==[1, 1]): yield k print(list(islice(agen(), 44))) # Michael S. Branicky, Nov 26 2022 CROSSREFS Cf. A001358, A006881, A124936, A358665. Sequence in context: A204193 A136919 A136920 * A274067 A069540 A366678 Adjacent sequences: A358683 A358684 A358685 * A358687 A358688 A358689 KEYWORD nonn AUTHOR Tanya Khovanova, Nov 26 2022 STATUS approved

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Last modified September 12 23:44 EDT 2024. Contains 375855 sequences. (Running on oeis4.)