A132858 Composite "antimutinous" numbers. An antimutinous number is an integer m > 1 where m/p^k < p, where p is the largest prime divisor of m and p^k is the largest power of p dividing m.

4, 6, 8, 9, 10, 14, 15, 16, 18, 20, 21, 22, 25, 26, 27, 28, 32, 33, 34, 35, 38, 39, 42, 44, 46, 49, 50, 51, 52, 54, 55, 57, 58, 62, 64, 65, 66, 68, 69, 74, 75, 76, 77, 78, 81, 82, 85, 86, 87, 88, 91, 92, 93, 94, 95, 98, 99, 100, 102, 104, 106, 110, 111, 114, 115, 116, 117, 118

Offset

1,1

Comments

{a(k)-1} is the complement of sequence A056077. In other words, {a(k)} contains precisely those positive integers m where A001142(m-1) (= product{k=1 to m-1} k^(2k-m)) is not divisible by all primes <= m-1.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mathematica

antiQ[n_] := Module[{f = FactorInteger[n], p, k}, p = f[[-1, 1]]; k = f[[-1, 2]]; n/p^k < p]; Select[Range[118], CompositeQ[#] && antiQ[#] &] (* Amiram Eldar, Feb 24 2020 *)

Crossrefs

Cf. A027855, A132982, A027854, A056077, A001142.

Sequence in context: A109104 A073303 A104211 * A071941 A188654 A330991

Adjacent sequences: A132855 A132856 A132857 * A132859 A132860 A132861

Keyword

nonn

Author

Leroy Quet, Nov 21 2007

Extensions

Extended by Ray Chandler, Nov 17 2008

Status

approved