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!)
 A332642 Numbers whose negated unsorted prime signature is not unimodal. 33
 90, 126, 198, 234, 270, 306, 342, 350, 378, 414, 522, 525, 540, 550, 558, 594, 630, 650, 666, 702, 738, 756, 774, 810, 825, 846, 850, 918, 950, 954, 975, 990, 1026, 1050, 1062, 1078, 1098, 1134, 1150, 1170, 1188, 1206, 1242, 1274, 1275, 1278, 1314, 1350, 1386 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A sequence of integers is unimodal if it is the concatenation of a weakly increasing and a weakly decreasing sequence. A number's prime signature (row n of A124010) is the sequence of positive exponents in its prime factorization. LINKS Eric Weisstein's World of Mathematics, Unimodal Sequence EXAMPLE The sequence of terms together with their prime indices begins:     90: {1,2,2,3}    126: {1,2,2,4}    198: {1,2,2,5}    234: {1,2,2,6}    270: {1,2,2,2,3}    306: {1,2,2,7}    342: {1,2,2,8}    350: {1,3,3,4}    378: {1,2,2,2,4}    414: {1,2,2,9}    522: {1,2,2,10}    525: {2,3,3,4}    540: {1,1,2,2,2,3}    550: {1,3,3,5}    558: {1,2,2,11}    594: {1,2,2,2,5}    630: {1,2,2,3,4}    650: {1,3,3,6}    666: {1,2,2,12}    702: {1,2,2,2,6} For example, 630 has negated unsorted prime signature (-1,-2,-1,-1), which is not unimodal, so 630 is in the sequence. MATHEMATICA unimodQ[q_]:=Or[Length[q]<=1, If[q[[1]]<=q[[2]], unimodQ[Rest[q]], OrderedQ[Reverse[q]]]] Select[Range[2000], !unimodQ[-Last/@FactorInteger[#]]&] CROSSREFS These are the Heinz numbers of the partitions counted by A332639. The case that is not unimodal either is A332643. The version for compositions is A332669. The complement is A332282. Unimodal compositions are A001523. Non-unimodal permutations are A059204. Non-unimodal compositions are A115981. Unsorted prime signature is A124010. Non-unimodal normal sequences are A328509. The number of non-unimodal negated permutations of a multiset whose multiplicities are the prime indices of n is A332742(n). Partitions whose negated 0-appended first differences are not unimodal are A332744, with Heinz numbers A332832. Cf. A007052, A056239, A112798, A181821, A242031, A329747, A332280, A332281, A332578, A332671, A332831. Sequence in context: A253385 A332831 A103653 * A249553 A125010 A241004 Adjacent sequences:  A332639 A332640 A332641 * A332643 A332644 A332645 KEYWORD nonn AUTHOR Gus Wiseman, Feb 28 2020 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 July 28 14:19 EDT 2021. Contains 346335 sequences. (Running on oeis4.)