A388989 Square array A(n,k) = A388991(A388981(n, k)), read by descending antidiagonals.

9, 16, 10, 15, 36, 28, 1, 28, 60, 264, 33, 44, 132, 4, 130, 45, 2, 13, 156, 924, 714, 48, 100, 102, 51, 51, 78, 304, 13, 24, 728, 24, 20, 1596, 765, 4140, 51, 17, 150, 2640, 1380, 1932, 3312, 152, 3828, 70, 76, 76, 588, 15860, 87, 261, 2610, 9660, 868, 19, 336, 276, 552, 1584, 60690, 1488, 1116, 2728, 6960, 1776

Offset

1,1

Comments

The array pair A388989 / A388990 gives the ratio A388988 / A388987 in its lowest terms.

Links

Antti Karttunen, Table of n, a(n) for n = 1..22155; the first 210 antidiagonals

Ratio A388989(n)/A388990(n) plotted with OEIS Plot tool

Index entries for sequences related to prime indices in the factorization of n.

Index entries for sequences related to sigma(n).

Example

The top left corner of the array:
k= |    1     2     3     4     5        6      7     8      9       10    11
---+--------------------------------------------------------------------------
1  |    9,   16,   15,    1,   33,      45,    48,   13,    51,      70,   19,
2  |   10,   36,   28,   44,    2,     100,    24,   17,    76,     336,   92,
3  |   28,   60,  132,   13,  102,     728,   150,   76,   276,    3060,   87,
4  |  264,    4,  156,   51,   24,    2640,   588,  552,   348,    2964,  744,
5  |  130,  924,   51,   20, 1380,   15860,  1584,  870,   620,  112464,   74,
6  |  714,   78, 1596, 1932,   87,   60690,  1170, 2604,   777,  317460, 1722,
7  |  304,  765, 3312,  261, 1488,   88160,   561,  148,  2952,  886788, 2064,
8  | 4140,  152, 2610, 1116, 3330, 1498680,  2660,  369,  7740, 1814196, 8460,
9  | 3828, 9660, 2728, 1628,  246, 2028840, 11040, 3784, 12408, 5116212, 6996,

Prog

(PARI)
up_to_cols = 210;
A326127(n) = (sigma(n)-core(n)-n);
A326128(n) = (n-core(n));
A388991(n) = { my(a=A326128(n)); (a / gcd(a, A326127(n))); };
A388984list(up_to) = { my(v=vector(up_to), i=0); forstep(n=2, oo, 2, if(isprime(core(n)) && !isprimepower(n), i++; v[i] = n; if(i==up_to, return(v)))); };
v388984 = A388984list(up_to_cols);
A388984(n) = v388984[n];
up_to = binomial(up_to_cols+1, 2)
A388981sq(row, col) = if(1==row, A388984(col), my(f = factor(A388984(col))); for(i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])+(row-1))); factorback(f));
A388989sq(row, col) = A388991(A388981sq(row, col));
A388989list(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] = A388989sq(col, (a-(col-1))))); (v); };
v388989 = A388989list(up_to);
A388989(n) = v388989[n];

Crossrefs

Cf. A388981, A388991.

Cf. also A388987, A388990 (denominators).

Sequence in context: A133816 A048752 A293376 * A169999 A110151 A131746

Adjacent sequences: A388986 A388987 A388988 * A388990 A388991 A388992

Keyword

nonn,frac,tabl

Author

Antti Karttunen, Sep 22 2025

Status

approved