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 A091155 Numbers n such that n - 2^k is squarefree for all 1 <= 2^k < n. 1
 2, 3, 4, 7, 15, 23, 39, 63, 75, 87, 111, 135, 147, 159, 195, 219, 231, 255, 267, 315, 387, 399, 411, 423, 435, 447, 459, 495, 519, 567, 615, 663, 675, 699, 711, 735, 747, 759, 771, 819, 867, 915, 999, 1011, 1023, 1035, 1047, 1071, 1095, 1119, 1155, 1167, 1263 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Erdos conjectures that this sequence is infinite. It appears that n = 3 (mod 12) except for n = 2, 4, 7 and 23. REFERENCES R. K. Guy, Unsolved Problems in Number Theory, A19. LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 P. Erdõs, On integers of the form 2^k + p and some related problems, Summa Brasil. Math. 2 (1950), pp. 113-123. EXAMPLE 39 is on the list because 38, 37, 35, 31, 23 and 7 are all squarefree. MATHEMATICA a={}; Do[k=1; While[sf=SquareFreeQ[n-k]; sf&&2k

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Last modified May 29 04:17 EDT 2020. Contains 334696 sequences. (Running on oeis4.)