login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A329637 Square array A(n, k) = A329644(prime(n)^k), read by falling antidiagonals: (1,1), (1,2), (2,1), (1,3), (2,2), (3,1), ... 5
1, 1, 1, 4, -1, 1, 0, 4, -5, 1, 24, -16, 4, -13, 1, -8, 40, -48, 4, -29, 1, 104, -88, 72, -112, 4, -61, 1, -48, 184, -248, 136, -240, 4, -125, 1, 352, -400, 344, -568, 264, -496, 4, -253, 1, 80, 544, -1104, 664, -1208, 520, -1008, 4, -509, 1, 1424, -784, 928, -2512, 1304, -2488, 1032, -2032, 4, -1021, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10440; the first 144 antidiagonals of array

Index entries for sequences related to sigma(n)

FORMULA

A(n, k) = A329644(A182944(n, k)).

A(n, k) = A000079(n+k-1) - (A000225(n) * A329890(k)).

EXAMPLE

The top left corner of the array:

   n   p_n |k=1,     2, 3,      4,     5,      6,     7,       8,      9,      10

  ---------+----------------------------------------------------------------------

   1 ->  2 |  1,     1, 4,      0,    24,     -8,   104,     -48,    352,      80,

   2 ->  3 |  1,    -1, 4,    -16,    40,    -88,   184,    -400,    544,    -784,

   3 ->  5 |  1,    -5, 4,    -48,    72,   -248,   344,   -1104,    928,   -2512,

   4 ->  7 |  1,   -13, 4,   -112,   136,   -568,   664,   -2512,   1696,   -5968,

   5 -> 11 |  1,   -29, 4,   -240,   264,  -1208,  1304,   -5328,   3232,  -12880,

   6 -> 13 |  1,   -61, 4,   -496,   520,  -2488,  2584,  -10960,   6304,  -26704,

   7 -> 17 |  1,  -125, 4,  -1008,  1032,  -5048,  5144,  -22224,  12448,  -54352,

   8 -> 19 |  1,  -253, 4,  -2032,  2056, -10168, 10264,  -44752,  24736, -109648,

   9 -> 23 |  1,  -509, 4,  -4080,  4104, -20408, 20504,  -89808,  49312, -220240,

  10 -> 29 |  1, -1021, 4,  -8176,  8200, -40888, 40984, -179920,  98464, -441424,

  11 -> 31 |  1, -2045, 4, -16368, 16392, -81848, 81944, -360144, 196768, -883792,

PROG

(PARI)

up_to = 105;

A329890(n) = if(1==n, 1, sigma((2^n)-1)-sigma((2^(n-1))-1));

A329637sq(n, k) = ((2^(n+k-1)) - (((2^n)-1) * A329890(k)));

A329637list(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] = A329637sq(col, (a-(col-1))))); (v); };

v329637 = A329637list(up_to);

A329637(n) = v329637[n];

CROSSREFS

Cf. A000079, A000203, A000225, A075708, A182944, A329610, A329644, A329890.

Rows 1-2: A329891, A329892 (from n>=1).

Column 1: A000012, Column 2: -A036563(n) (from n>=1), Column 3: A010709.

Sequence in context: A135302 A128760 A057884 * A276834 A016684 A324564

Adjacent sequences:  A329634 A329635 A329636 * A329638 A329639 A329640

KEYWORD

sign,tabl

AUTHOR

Antti Karttunen, Nov 22 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 24 07:00 EDT 2021. Contains 345416 sequences. (Running on oeis4.)