A132982 The non-prime-power "antimutinous" numbers. (Antimutinous numbers are those integers m, m >1, where m/p^k < p, p = largest prime divisor of m, p^k = largest power of p that divides m.)

6, 10, 14, 15, 18, 20, 21, 22, 26, 28, 33, 34, 35, 38, 39, 42, 44, 46, 50, 51, 52, 54, 55, 57, 58, 62, 65, 66, 68, 69, 74, 75, 76, 77, 78, 82, 85, 86, 87, 88, 91, 92, 93, 94, 95, 98, 99, 100, 102, 104, 106, 110, 111, 114, 115, 116, 117, 118, 119, 122, 123, 124, 129, 130

Offset

1,1

Links

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

Example

30 = 2*3*5. 2*3 is > 5, so 30 is not in the sequence because 30 is mutinous (see A027854).
27 = 3^3. 27/3^3 is < 3, so 27 is antimutinous. But 27 is a power of a prime, so 27 is not in the sequence.
However, 20 = 2^2 * 5^1. And 20/5^1 is < 5, so 20 is antimutinous. Also, 20 is not a power of a prime. So 20 is in the sequence.

Mathematica

a = {}; For[n = 2, n < 200, n++, If[ !PrimeQ[n], If[ ! Length[FactorInteger[n]] == 1, b = FactorInteger[n]; m = 0; For[j = 1, j < Length[b] + 1, j++, If[b[[j, 1]]^b[[j, 2]] > m, m = b[[j, 1]]^b[[j, 2]]]; If[n/m < FactorInteger[m][[1, 1]], AppendTo[a, n]]]]]]; a (* Stefan Steinerberger, Nov 20 2007 *)

Crossrefs

Cf. A027854, A027855.

Sequence in context: A085234 A057714 A143907 * A354922 A300080 A069169

Adjacent sequences: A132979 A132980 A132981 * A132983 A132984 A132985

Keyword

nonn

Author

Leroy Quet, Nov 19 2007

Extensions

More terms from Stefan Steinerberger, Nov 20 2007

Status

approved