The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A325281 Numbers of the form a*b, a*a*b, or a*a*b*c where a, b, and c are distinct primes. Numbers with sorted prime signature (1,1), (1,2), or (1,1,2). 5
 6, 10, 12, 14, 15, 18, 20, 21, 22, 26, 28, 33, 34, 35, 38, 39, 44, 45, 46, 50, 51, 52, 55, 57, 58, 60, 62, 63, 65, 68, 69, 74, 75, 76, 77, 82, 84, 85, 86, 87, 90, 91, 92, 93, 94, 95, 98, 99, 106, 111, 115, 116, 117, 118, 119, 122, 123, 124, 126, 129, 132 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Also numbers whose adjusted frequency depth is one plus their number of prime factors counted with multiplicity. The adjusted frequency depth of a positive integer n is 0 if n = 1, and otherwise it is one plus the number of times one must apply A181819 to reach a prime number, where A181819(k = p^i*...*q^j) = prime(i)*...*prime(j) = product of primes indexed by the prime exponents of k. For example, 180 has adjusted frequency depth 5 because we have: 180 -> 18 -> 6 -> 4 -> 3. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are Heinz numbers of integer partitions whose adjusted frequency depth is equal to their length plus 1. The enumeration of these partitions by sum is given by A127002. LINKS Table of n, a(n) for n=1..61. EXAMPLE The sequence of terms together with their prime indices and their omega-sequences (see A323023) begins: 6: {1,2} (2,2,1) 10: {1,3} (2,2,1) 12: {1,1,2} (3,2,2,1) 14: {1,4} (2,2,1) 15: {2,3} (2,2,1) 18: {1,2,2} (3,2,2,1) 20: {1,1,3} (3,2,2,1) 21: {2,4} (2,2,1) 22: {1,5} (2,2,1) 26: {1,6} (2,2,1) 28: {1,1,4} (3,2,2,1) 33: {2,5} (2,2,1) 34: {1,7} (2,2,1) 35: {3,4} (2,2,1) 38: {1,8} (2,2,1) 39: {2,6} (2,2,1) 44: {1,1,5} (3,2,2,1) 45: {2,2,3} (3,2,2,1) 46: {1,9} (2,2,1) 50: {1,3,3} (3,2,2,1) 51: {2,7} (2,2,1) 52: {1,1,6} (3,2,2,1) 55: {3,5} (2,2,1) 57: {2,8} (2,2,1) 58: {1,10} (2,2,1) 60: {1,1,2,3} (4,3,2,2,1) MATHEMATICA fdadj[n_Integer]:=If[n==1, 0, Length[NestWhileList[Times@@Prime/@Last/@FactorInteger[#]&, n, !PrimeQ[#]&]]]; Select[Range[100], fdadj[#]==PrimeOmega[#]+1&] CROSSREFS Cf. A056239, A112798, A118914, A127002, A181819, A323023, A325246, A325259, A325266, A325270, A325277, A325282. Omega-sequence statistics: A001222 (first omega), A001221 (second omega), A071625 (third omega), A323022 (fourth omega), A304465 (second-to-last omega), A182850 or A323014 (length/frequency depth), A325248 (Heinz number), A325249 (sum). Sequence in context: A237051 A340749 A296205 * A100658 A182301 A069059 Adjacent sequences: A325278 A325279 A325280 * A325282 A325283 A325284 KEYWORD nonn AUTHOR Gus Wiseman, Apr 18 2019 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 June 18 17:09 EDT 2024. Contains 373482 sequences. (Running on oeis4.)