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.
%I A060177 #36 Sep 15 2023 10:21:02
%S A060177 1,2,1,2,2,3,5,2,1,6,4,2,11,2,5,13,4,10,17,3,1,15,22,4,2,25,27,2,5,37,
%T A060177 29,6,10,52,37,2,20,67,44,4,1,30,97,44,4,2,52,117,55,5,5,77,154,59,2,
%U A060177 10,117,184,68,6,20,162,235,71,2,36,227,277,81,6,1,58,309,338
%N A060177 Triangle of generalized sum of divisors function, read by rows.
%C A060177 Lengths of rows are 1 1 2 2 2 3 3 3 3 4 4 4 4 4 ... (A003056).
%H A060177 Alois P. Heinz, <a href="/A060177/b060177.txt">Rows n = 1..500, flattened</a>
%H A060177 P. A. MacMahon, <a href="https://doi.org/10.1112/plms/s2-19.1.75">Divisors of numbers and their continuations in the theory of partitions</a>, Proc. London Math. Soc., (2) 19 (1919), 75-113; Coll. Papers II, pp. 303-341.
%F A060177 T(n,k) = Partitions of n using only k types of piles. Also, Sum_{k=1..A003056(n)} T(n,k)*k = A000070(n). Also, Sum_{k=1..A003056(n)} T(n,k)*(k-1) = A058884(n). - _Naohiro Nomoto_, Jan 24 2002
%F A060177 G.f. for k-th diagonal (the k-th row of the sideways triangle shown in the example): Sum_{ m_1 < m_2 < ... < m_k} q^(m_1+m_2+...+m_k)/((1-q^m_1)*(1-q^m_2)*...*(1-q^m_k)) = Sum_n T(n, k)*q^n.
%e A060177 Triangle turned on its side begins:
%e A060177 1 2 2 3 2 4 2 4 3 4 2 6 ...
%e A060177 1 2 5 6 11 13 17 22 27 29 ...
%e A060177 1 2 5 10 15 25 37 ...
%e A060177 1 2 5 ...
%p A060177 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A060177 expand(b(n, i-1) +x*add(b(n-i*j, i-1), j=1..n/i))))
%p A060177 end:
%p A060177 T:= n->(p->seq(coeff(p, x, degree(p)-k), k=0..degree(p)-1))(b(n$2)):
%p A060177 seq(T(n), n=1..25); # _Alois P. Heinz_, Jan 29 2014
%t A060177 Reverse /@ Table[Length /@ Split[ Sort[Map[Length, Split /@ IntegerPartitions[n], {1}]]], {n, 24}] (* _Wouter Meeussen_, Apr 21 2012, updated by _Jean-François Alcover_, Jan 29 2014 *)
%o A060177 (Python)
%o A060177 from math import isqrt
%o A060177 from itertools import count, islice
%o A060177 from sympy.utilities.iterables import partitions
%o A060177 def A060177_gen(): # generator of terms
%o A060177 return (sum(1 for p in partitions(n) if len(p)==k) for n in count(1) for k in range(isqrt((n<<3)+1)-1>>1,0,-1))
%o A060177 A060177_list = list(islice(A060177_gen(),30)) # _Chai Wah Wu_, Sep 15 2023
%Y A060177 Diagonals give A000005, A002133, A002134, A365630, A365631. Cf. A060043, A060044.
%Y A060177 Cf. A116608 (reflected rows). - _Alois P. Heinz_, Jan 29 2014
%K A060177 nonn,tabf,easy,nice,look
%O A060177 1,2
%A A060177 _N. J. A. Sloane_, Mar 20 2001
%E A060177 More terms from _Naohiro Nomoto_, Jan 24 2002