cp's OEIS Frontend

A129305 Encodes multisets of least prime signatures in reverse-lex order: replace A036035 with A080688 then calculate all possible factorizations of the resulting values, recode each factor using A064553(n) and then multiply the terms.

%I A129305 #12 Sep 12 2024 14:39:50
%S A129305 1,2,4,5,6,11,8,10,17,12,15,22,31,42,69,77,86,109,16,20,25,34,47,24,
%T A129305 30,44,55,51,62,83,36,45,66,76,95,121,93,118,149,84,105,138,154,172,
%U A129305 215,253,201,217,218,277,546,834,861,897,994,1001,1118,1529,1633,1763,1041
%N A129305 Encodes multisets of least prime signatures in reverse-lex order: replace A036035 with A080688 then calculate all possible factorizations of the resulting values, recode each factor using A064553(n) and then multiply the terms.
%C A129305 Sequence A035310 counts the values in each subtable and illustrates relationships with A000041, A000079, A000110 etc. Sequence A096443 counts the values associated with each least prime signature. (Cf. A025487 and A036035.)
%e A129305 The encoded values can be arranged in tabular form based on the number of factors and the associated numeric partitions as indicated below:
%e A129305 2..................................................
%e A129305 .....4.....5........................................
%e A129305 .....6.....11........................................
%e A129305 ...............8.....10.....17.........................
%e A129305 ...............12....15.....31.........................
%e A129305 .....................22..............................
%e A129305 ...............42....69.....109.........................
%e A129305 .....................77..............................
%e A129305 .....................86..............................
%e A129305 .................................16.....20.....25.....34.....47
%e A129305 .................................24.....30.....55.....51.....83
%e A129305 ........................................44............62.....
%e A129305 .................................36.....45.....95.....93.....149
%e A129305 ........................................66.....121...118.....
%e A129305 ........................................76...............
%e A129305 .................................84.....105.....215.....201.....277
%e A129305 ........................................138.....253.....217.....
%e A129305 ........................................154.............218.....
%e A129305 ........................................172...............
%e A129305 ................................546.....834.....1529.....1041.....1289
%e A129305 ........................................861.....1633.....1138.....
%e A129305 ........................................897.....1763.....1253.....
%e A129305 ........................................994..............1417.....
%e A129305 ........................................1001...............
%e A129305 ........................................1118...............
%Y A129305 Cf. A025487, A035310, A036035, A064553, A080688, A096443.
%K A129305 nonn
%O A129305 0,2
%A A129305 _Alford Arnold_, May 02 2007