The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A322833 Squarefree MM-numbers of strict uniform regular multiset multisystems. Squarefree numbers whose prime indices all have the same number of prime factors counted with multiplicity, and such that the product of the same prime indices is a power of a squarefree number. 3
 1, 2, 3, 5, 7, 11, 13, 15, 17, 19, 23, 29, 31, 33, 41, 43, 47, 51, 53, 55, 59, 67, 73, 79, 83, 85, 93, 97, 101, 103, 109, 113, 123, 127, 131, 137, 139, 149, 151, 155, 157, 161, 163, 165, 167, 177, 179, 181, 187, 191, 199, 201, 205, 211, 227, 233, 241, 249, 255 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A multiset multisystem is a finite multiset of finite multisets. 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 multiset multisystem with MM-number n is formed by taking the multiset of prime indices of each part of the multiset of prime indices of n. For example, the prime indices of 78 are {1,2,6}, so the multiset multisystem with MM-number 78 is {{},{1},{1,2}}. A multiset multisystem is uniform if all parts have the same size, regular if all vertices appear the same number of times, and strict if there are no repeated parts. For example, {{1,2,2},{1,3,3}} is uniform, regular, and strict, so its MM-number 13969 belongs to the sequence. Note that the parts of parts such as {1,2,2} do not have to be distinct, only the multiset of parts. LINKS EXAMPLE The sequence of all strict uniform regular multiset multisystems, together with their MM-numbers, begins:    1: {}           59: {{7}}         157: {{12}}        269: {{2,8}}    2: {{}}         67: {{8}}         161: {{1,1},{2,2}} 271: {{1,10}}    3: {{1}}        73: {{2,4}}       163: {{1,8}}       277: {{17}}    5: {{2}}        79: {{1,5}}       165: {{1},{2},{3}} 283: {{18}}    7: {{1,1}}      83: {{9}}         167: {{2,6}}       293: {{1,11}}   11: {{3}}        85: {{2},{4}}     177: {{1},{7}}     295: {{2},{7}}   13: {{1,2}}      93: {{1},{5}}     179: {{13}}        311: {{1,1,1,1,1,1}}   15: {{1},{2}}    97: {{3,3}}       181: {{1,2,4}}     313: {{3,6}}   17: {{4}}       101: {{1,6}}       187: {{3},{4}}     317: {{1,2,5}}   19: {{1,1,1}}   103: {{2,2,2}}     191: {{14}}        327: {{1},{10}}   23: {{2,2}}     109: {{10}}        199: {{1,9}}       331: {{19}}   29: {{1,3}}     113: {{1,2,3}}     201: {{1},{8}}     335: {{2},{8}}   31: {{5}}       123: {{1},{6}}     205: {{2},{6}}     341: {{3},{5}}   33: {{1},{3}}   127: {{11}}        211: {{15}}        347: {{2,9}}   41: {{6}}       131: {{1,1,1,1,1}} 227: {{4,4}}       349: {{1,3,4}}   43: {{1,4}}     137: {{2,5}}       233: {{2,7}}       353: {{20}}   47: {{2,3}}     139: {{1,7}}       241: {{16}}        367: {{21}}   51: {{1},{4}}   149: {{3,4}}       249: {{1},{9}}     373: {{1,12}}   53: {{1,1,1,1}} 151: {{1,1,2,2}}   255: {{1},{2},{4}} 381: {{1},{11}}   55: {{2},{3}}   155: {{2},{5}}     257: {{3,5}}       389: {{4,5}} MATHEMATICA primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; Select[Range[100], And[SquareFreeQ[#], SameQ@@PrimeOmega/@primeMS[#], SameQ@@Last/@FactorInteger[Times@@primeMS[#]]]&] CROSSREFS Cf. A005117, A007016, A112798, A302242, A306017, A319056, A319189, A320324, A321698, A321699, A322554, A322703. Sequence in context: A319327 A319319 A003277 * A117287 A121615 A097605 Adjacent sequences:  A322830 A322831 A322832 * A322834 A322835 A322836 KEYWORD nonn AUTHOR Gus Wiseman, Dec 27 2018 STATUS approved

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

Last modified April 5 06:13 EDT 2020. Contains 333238 sequences. (Running on oeis4.)