cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A319073 Square array read by antidiagonals upwards: T(n,k) = k*sigma(n), n >= 1, k >= 1.

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%I A319073 #29 Jan 08 2019 08:38:45
%S A319073 1,3,2,4,6,3,7,8,9,4,6,14,12,12,5,12,12,21,16,15,6,8,24,18,28,20,18,7,
%T A319073 15,16,36,24,35,24,21,8,13,30,24,48,30,42,28,24,9,18,26,45,32,60,36,
%U A319073 49,32,27,10,12,36,39,60,40,72,42,56,36,30,11,28,24,54,52,75,48,84,48,63,40,33,12
%N A319073 Square array read by antidiagonals upwards: T(n,k) = k*sigma(n), n >= 1, k >= 1.
%H A319073 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%e A319073 The corner of the square array begins:
%e A319073          A000203 A074400 A272027 A239050 A274535 A274536 A319527 A319528
%e A319073 A000027:       1,      2,      3,      4,      5,      6,      7,      8, ...
%e A319073 A008585:       3,      6,      9,     12,     15,     18,     21,     24, ...
%e A319073 A008586:       4,      8,     12,     16,     20,     24,     28,     32, ...
%e A319073 A008589:       7,     14,     21,     28,     35,     42,     49,     56, ...
%e A319073 A008588:       6,     12,     18,     24,     30,     36,     42,     48, ...
%e A319073 A008594:      12,     24,     36,     48,     60,     72,     84,     96, ...
%e A319073 A008590:       8,     16,     24,     32,     40,     48,     56,     64, ...
%e A319073 A008597:      15,     30,     45,     60,     75,     90,    105,    120, ...
%e A319073 A008595:      13,     26,     39,     52,     65,     78,     91,    104, ...
%e A319073 A008600:      18,     36,     54,     72,     90,    108,    126,    144, ...
%e A319073 ...
%p A319073 with(numtheory): T:=(n,k)->k*sigma(n-k+1): seq(seq(T(n,k),k=1..n),n=1..12); # _Muniru A Asiru_, Jan 01 2019
%t A319073 Table[k DivisorSigma[1, #] &[m - k + 1], {m, 12}, {k, m}] // Flatten (* _Michael De Vlieger_, Dec 31 2018 *)
%o A319073 (GAP) T:=Flat(List([1..12],n->List([1..n],k->k*Sigma(n-k+1))));; Print(T); # _Muniru A Asiru_, Jan 01 2019
%Y A319073 Another version of A274824.
%Y A319073 Antidiagonal sums give A175254.
%Y A319073 Main diagonal gives A064987.
%Y A319073 Row n lists the multiples of A000203(n).
%Y A319073 Row 1 is A000027.
%Y A319073 Initial zeros should be omitted in the following sequences related to the rows of the array:
%Y A319073 Row 2-5: A008585, A008586, A008589, A008588.
%Y A319073 Rows 6 and 11: A008594.
%Y A319073 Rows 7-9: A008590, A008597, A008595.
%Y A319073 Rows 10 and 17: A008600.
%Y A319073 Rows 12-13: A135628, A008596.
%Y A319073 Rows 14, 15 and 23: A008606.
%Y A319073 Rows 16 and 25: A135631.
%Y A319073 (Note that in the OEIS there are many other sequences that are also rows of this square array.)
%Y A319073 Cf. A000203, A237593, A319526.
%K A319073 nonn,tabl,easy
%O A319073 1,2
%A A319073 _Omar E. Pol_, Sep 22 2018