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

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A325284 Numbers whose prime indices form an initial interval with a single hole: (1, 2, ..., x, x + 2, ..., m - 1, m), where x can be 0 but must be less than m - 1. 4
3, 9, 10, 15, 20, 27, 40, 42, 45, 50, 70, 75, 80, 81, 84, 100, 105, 126, 135, 140, 160, 168, 200, 225, 243, 250, 252, 280, 294, 315, 320, 330, 336, 350, 375, 378, 400, 405, 462, 490, 500, 504, 525, 560, 588, 640, 660, 672, 675, 700, 729, 735, 756, 770, 800 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
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 distinct parts form an initial interval with a single hole. The enumeration of these partitions by sum is given by A090858.
LINKS
EXAMPLE
The sequence of terms together with their prime indices begins:
3: {2}
9: {2,2}
10: {1,3}
15: {2,3}
20: {1,1,3}
27: {2,2,2}
40: {1,1,1,3}
42: {1,2,4}
45: {2,2,3}
50: {1,3,3}
70: {1,3,4}
75: {2,3,3}
80: {1,1,1,1,3}
81: {2,2,2,2}
84: {1,1,2,4}
100: {1,1,3,3}
105: {2,3,4}
126: {1,2,2,4}
135: {2,2,2,3}
140: {1,1,3,4}
MATHEMATICA
Select[Range[100], Length[Complement[Range[PrimePi[FactorInteger[#][[-1, 1]]]], PrimePi/@First/@FactorInteger[#]]]==1&]
CROSSREFS
Sequence in context: A191339 A138923 A324584 * A049096 A272653 A030794
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 19 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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 20 21:11 EDT 2024. Contains 371845 sequences. (Running on oeis4.)