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 A328524 T(n,k) is the k-th smallest least integer of prime signatures for partitions of n into distinct parts; triangle T(n,k), n>=0, 1<=k<=A000009(n), read by rows. 5
 1, 2, 4, 8, 12, 16, 24, 32, 48, 72, 64, 96, 144, 360, 128, 192, 288, 432, 720, 256, 384, 576, 864, 1440, 2160, 512, 768, 1152, 1728, 2592, 2880, 4320, 10800, 1024, 1536, 2304, 3456, 5184, 5760, 8640, 12960, 21600, 75600, 2048, 3072, 4608, 6912, 10368, 11520 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Rows n = 0..50, flattened Eric Weisstein's World of Mathematics, Prime Signature Wikipedia, Partition (number theory) Wikipedia, Prime signature Index entries for sequences related to prime signature EXAMPLE Triangle T(n,k) begins: 1; 2; 4; 8, 12; 16, 24; 32, 48, 72; 64, 96, 144, 360; 128, 192, 288, 432, 720; 256, 384, 576, 864, 1440, 2160; 512, 768, 1152, 1728, 2592, 2880, 4320, 10800; 1024, 1536, 2304, 3456, 5184, 5760, 8640, 12960, 21600, 75600; ... MAPLE b:= proc(n, i, j) option remember; `if`(i*(i+1)/2 x*ithprime(j)^i, b(n-i, min(n-i, i-1), j+1))[], b(n, i-1, j)[]])) end: T:= n-> sort(b(n\$2, 1))[]: seq(T(n), n=0..12); MATHEMATICA b[n_, i_, j_] := b[n, i, j] = If[i(i+1)/2 < n, {}, If[n == 0, {1}, Join[# * Prime[j]^i& /@ b[n - i, Min[n - i, i - 1], j + 1], b[n, i - 1, j]]]]; T[n_] := Sort[b[n, n, 1]]; Table[T[n], {n, 0, 12}] // Flatten (* Jean-François Alcover, May 07 2020, after Maple *) CROSSREFS Column k=1-3 give: A000079, A003945 for n>2, A116453 for n>4. Row sums give A332626. Last elements of rows give A332644. Cf. A000009, A087443 (for all partitions), A087980 (as sorted sequence). Sequence in context: A363063 A336496 A317804 * A322447 A170892 A246468 Adjacent sequences: A328521 A328522 A328523 * A328525 A328526 A328527 KEYWORD nonn,tabf AUTHOR Alois P. Heinz, Feb 18 2020 STATUS approved

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Last modified April 15 10:24 EDT 2024. Contains 371681 sequences. (Running on oeis4.)