cp's OEIS Frontend

A379011 Square array A(n, k) = 2*phi(A246278(n, k)) - A246278(n, k), read by falling antidiagonals; A083254, (2*phi(n)-n), applied to the prime shift array.

%I A379011 #9 Dec 14 2024 11:01:20
%S A379011 0,0,1,-2,3,3,0,1,15,5,-2,9,13,35,9,-4,3,75,43,99,11,-2,3,25,245,97,
%T A379011 143,15,0,7,65,53,1089,163,255,17,-6,27,31,301,133,1859,253,323,21,-4,
%U A379011 5,375,73,1067,185,4335,355,483,27,-2,9,91,1715,151,2119,313,6137,565,783,29,-8,9,125,473,11979,229,4301,457,11109,781,899,35
%N A379011 Square array A(n, k) = 2*phi(A246278(n, k)) - A246278(n, k), read by falling antidiagonals; A083254, (2*phi(n)-n), applied to the prime shift array.
%C A379011 Each column is strictly increasing.
%H A379011 Antti Karttunen, <a href="/A379011/b379011.txt">Table of n, a(n) for n = 1..11325; the first 150 antidiagonals, flattened</a>
%H A379011 <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>.
%F A379011 A(n, k) = 2*A379010(n, k) - A246278(n, k).
%e A379011 The top left corner of the array:
%e A379011 k=  |  1    2    3      4    5      6    7       8      9     10   11      12
%e A379011 2k= |  2    4    6      8   10     12   14      16     18     20   22      24
%e A379011 ----+-------------------------------------------------------------------------
%e A379011   1 |  0,   0,  -2,     0,  -2,    -4,  -2,      0,    -6,    -4,  -2,     -8,
%e A379011   2 |  1,   3,   1,     9,   3,     3,   7,     27,     5,     9,   9,      9,
%e A379011   3 |  3,  15,  13,    75,  25,    65,  31,    375,    91,   125,  43,    325,
%e A379011   4 |  5,  35,  43,   245,  53,   301,  73,   1715,   473,   371,  83,   2107,
%e A379011   5 |  9,  99,  97,  1089, 133,  1067, 151,  11979,  1261,  1463, 187,  11737,
%e A379011   6 | 11, 143, 163,  1859, 185,  2119, 229,  24167,  2771,  2405, 295,  27547,
%e A379011   7 | 15, 255, 253,  4335, 313,  4301, 403,  73695,  4807,  5321, 433,  73117,
%e A379011   8 | 17, 323, 355,  6137, 457,  6745, 491, 116603,  8165,  8683, 593, 128155,
%e A379011   9 | 21, 483, 565, 11109, 607, 12995, 733, 255507, 16385, 13961, 817, 298885,
%o A379011 (PARI)
%o A379011 up_to = 11325; \\ = binomial(150+1,2)
%o A379011 A083254(n) = (2*eulerphi(n)-n);
%o A379011 A246278sq(row,col) = if(1==row,2*col, my(f = factor(2*col)); for(i=1, #f~, f[i,1] = prime(primepi(f[i,1])+(row-1))); factorback(f));
%o A379011 A379011sq(row,col) = A083254(A246278sq(row,col));
%o A379011 A379011list(up_to) = { my(v = vector(up_to), i=0); for(a=1,oo, for(col=1,a, i++; if(i > up_to, return(v)); v[i] = A379011sq(col,(a-(col-1))))); (v); };
%o A379011 v379011 = A379011list(up_to);
%o A379011 A379011(n) = v379011[n];
%Y A379011 Cf. A000010, A083254, A246278, A379010.
%Y A379011 Cf. A040976 (column 1), A378986 (row 1).
%Y A379011 Cf. also A378979.
%K A379011 sign,tabl
%O A379011 1,4
%A A379011 _Antti Karttunen_, Dec 14 2024