cp's OEIS Frontend

A337472 Square array read by falling antidiagonals, where A(n,k) = sigma(A337470(n, k)).

%I A337472 #9 Aug 28 2020 11:07:28
%S A337472 1,3,1,12,4,1,7,24,6,1,72,13,48,8,1,28,192,31,96,12,1,576,78,576,57,
%T A337472 168,14,1,15,2304,248,1344,133,252,18,1,91,40,8064,684,3024,183,360,
%U A337472 20,1,168,403,156,24192,1862,5040,307,480,24,1,6912,624,1767,400,60480,3294,8640,381,720,30,1
%N A337472 Square array read by falling antidiagonals, where A(n,k) = sigma(A337470(n, k)).
%C A337472 Array is read by descending antidiagonals with n >= 0 and k >= 1 ranging as: (0, 1), (0, 2), (1, 1), (0, 3), (1, 2), (2, 1), (0, 4), (1, 3), (2, 2), (3, 1), ...
%H A337472 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A337472 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>
%H A337472 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A337472 A(n,k) = A000203(A337470(n, k)).
%e A337472 The top left corner of the array begins as:
%e A337472 n/k | 1   2    3    4     5     6       7     8      9     10
%e A337472 ----|--------------------------------------------------------------
%e A337472   0 | 1,  3,  12,   7,   72,   28,    576,   15,    91,   168, ...
%e A337472   1 | 1,  4,  24,  13,  192,   78,   2304,   40,   403,   624, ...
%e A337472   2 | 1,  6,  48,  31,  576,  248,   8064,  156,  1767,  2976, ...
%e A337472   3 | 1,  8,  96,  57, 1344,  684,  24192,  400,  7581,  9576, ...
%e A337472   4 | 1, 12, 168, 133, 3024, 1862,  60480, 1464, 24339, 33516, ...
%e A337472   5 | 1, 14, 252, 183, 5040, 3294, 120960, 2380, 56181, 65880, ...
%e A337472 etc.
%o A337472 (PARI)
%o A337472 up_to = 105-1; \\ Or 78-1.
%o A337472 Ashifted_primorial(n,d) = prod(i=1, primepi(n), prime(i+d));
%o A337472 A337470sq(n, k) = { my(f=factor(k)); prod(i=1, #f~, Ashifted_primorial(f[i, 1], n)^f[i, 2]); };
%o A337472 A337472sq(n, k) = sigma(A337470sq(n, k));
%o A337472 A337472list(up_to) = { my(v = vector(1+up_to), i=0); for(a=0, oo, for(b=1, a, i++; if(i > #v, return(v)); v[i] = A337472sq(b-1, (a-(b-1))))); (v); };
%o A337472 v337472 = A337472list(up_to);
%o A337472 A337472(n) = v337472[1+n];
%Y A337472 Cf. A000203, A003961.
%Y A337472 Cf. A337203 (row 0).
%Y A337472 Cf. also arrays A337205, A337470.
%K A337472 nonn,tabl
%O A337472 0,2
%A A337472 _Antti Karttunen_, Aug 28 2020