The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A369118 k is term if and only if k is a composite number where the bases and the exponents of its factors in the prime decomposition are all odd primes. 1
 27, 125, 243, 343, 1331, 2187, 2197, 3125, 3375, 4913, 6859, 9261, 12167, 16807, 24389, 29791, 30375, 35937, 42875, 50653, 59319, 68921, 78125, 79507, 83349, 84375, 103823, 132651, 148877, 161051, 166375, 177147, 185193, 205379, 226981, 273375, 274625 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Every term is divisible by a cube. If n and k are terms then n*k is a term if and only if gcd(n, k) = 1. From Michael De Vlieger, Jan 19 2024: (Start) Prime exponents of prime power factors p^m | k imply that k is a powerful number. Hence this sequence is a proper subset of A001694, and k is of the form a^2 * b^3. Prime exponents m imply either perfect powers k in A001597 such that all the m are the same, or an Achilles number k (in A052486) if the exponents differ. This is because prime p divides itself but is coprime to primes q != p. Therefore this sequence is not a subsequence of A001597. The sequence consists of composite prime powers (A246547) and powerful numbers that are not prime powers (A286708), both of which are numbers that are not squarefree (A013929). (End) LINKS Michael De Vlieger, Table of n, a(n) for n = 1..10000 EXAMPLE 25015118625 = 3^5 * 5^3 * 7^7 is a term. 3125 = 5^5 and 3375 = 3^3 * 5^3 are terms but 3125*3375 is not a term. MATHEMATICA A369118Q[n_] := OddQ[n] && AllTrue[FactorInteger[n], OddQ[#] && PrimeQ[#]&, 2]; Select[Range[500000], A369118Q] (* Paolo Xausa, Jan 19 2024 *) PROG (SageMath) def isA369118(n): return (n > 1 and is_odd(n) and all(is_odd(f[1]) and is_prime(f[1]) for f in factor(n))) print([n for n in range(1, 300000) if isA369118(n)]) CROSSREFS Cf. A002808 (superset), A001694 (superset). A051674 is a subsequence for n>1. Intersects A001597, A013929, A052486, A246547, A286708. Sequence in context: A137800 A125497 A179145 * A118092 A371189 A126272 Adjacent sequences: A369115 A369116 A369117 * A369119 A369120 A369121 KEYWORD nonn AUTHOR Peter Luschny, Jan 17 2024 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 12 19:59 EDT 2024. Contains 374252 sequences. (Running on oeis4.)