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A117851 Numbers n such that n^3 is of the form semiprime(k) + k-th composite number. 0
2, 3, 4, 6, 7, 10, 29, 30, 33, 35, 36, 41, 42, 46, 53, 61, 72, 74, 77, 82, 88, 99, 106, 121, 123, 127, 133, 146, 150, 159, 164, 170, 175, 180, 194, 214, 221, 231, 233, 248, 257, 262, 267, 271, 274, 278, 287, 289, 290, 303, 304, 308, 311, 316, 318, 324 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Corresponding k's: 1, 6, 15, 50, 78, 219, 4803, 5303, 6973, 8261, 8968, 13058, 13972, 18210, 27426, 41167, ...,.

LINKS

Table of n, a(n) for n=1..56.

FORMULA

Cuberoot(A112662(n)).

MATHEMATICA

Composite[n_Integer] := FixedPoint[n + PrimePi@# + 1 &, n + PrimePi@n + 1]; SemiPrimePi[n_] := Sum[PrimePi[n/Prime@i] - i + 1, {i, PrimePi@Sqrt@n}]; SemiPrime[n_] := Block[{e = Floor[Log[2, n] + 1], a, b}, a = 2^e; Do[b = 2^p; While[SemiPrimePi[a] < n, a = a + b]; a = a - b/2, {p, e, 0, -1}]; a + b/2]; lst = {}; Do[c = Composite@n + SemiPrime@n; If[IntegerQ[c^(1/3)], Print[c]], {n, 10^7}]; lst (* Robert G. Wilson v *)

CROSSREFS

Sequence in context: A194855 A272766 A271340 * A050679 A158806 A184966

Adjacent sequences:  A117848 A117849 A117850 * A117852 A117853 A117854

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, May 01 2006

STATUS

approved

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Last modified December 10 15:32 EST 2016. Contains 279003 sequences.