A388982 Square array A(n,k), read by descending antidiagonals, where A(1, k) = A388980(k), and for n > 1, A(n, k) = A003961(A(n-1), k).

2, 8, 3, 12, 27, 5, 18, 45, 125, 7, 20, 75, 175, 343, 11, 28, 63, 245, 539, 1331, 13, 32, 99, 275, 847, 1573, 2197, 17, 44, 243, 325, 637, 1859, 2873, 4913, 19, 48, 117, 3125, 833, 2057, 3757, 5491, 6859, 23, 50, 405, 425, 16807, 2299, 3211, 6137, 8303, 12167, 29, 52, 147, 4375, 931, 161051, 3887, 6647, 10051, 15341, 24389, 31

Offset

1,1

Comments

This is otherwise like the primeshift array A246278, but includes only those columns of it that contain numbers of the form p * m^2, where p is prime and m > 0, i.e., numbers k such that A007913(k) is a prime.

Links

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

Index entries for sequences computed from indices in prime factorization.

Formula

A(n, k) = A246278(n, A388980(k)/2).

Example

The top left corner of the array:
k=  |  1      2      3      4      5      6         7      8         9     10
----+-------------------------------------------------------------------------
1   |  2,     8,    12,    18,    20,    28,       32,    44,       48,    50,
2   |  3,    27,    45,    75,    63,    99,      243,   117,      405,   147,
3   |  5,   125,   175,   245,   275,   325,     3125,   425,     4375,   605,
4   |  7,   343,   539,   847,   637,   833,    16807,   931,    26411,  1183,
5   | 11,  1331,  1573,  1859,  2057,  2299,   161051,  2783,   190333,  3179,
6   | 13,  2197,  2873,  3757,  3211,  3887,   371293,  4901,   485537,  4693,
7   | 17,  4913,  5491,  6137,  6647,  8381,  1419857,  8959,  1586899,  8993,
8   | 19,  6859,  8303, 10051, 10469, 11191,  2476099, 13357,  2997383, 15979,
9   | 23, 12167, 15341, 19343, 16399, 19573,  6436343, 21689,  8115389, 22103,
10  | 29, 24389, 26071, 27869, 31117, 34481, 20511149, 36163, 21925711, 39701,

Prog

(PARI)
up_to_cols = 210;
A388980list(up_to) = { my(v=vector(up_to), i=0); forstep(n=2, oo, 2, if(isprime(core(n)), i++; v[i] = n; if(i==up_to, return(v)))); };
v388980 = A388980list(up_to_cols);
A388980(n) = v388980[n];
up_to = binomial(up_to_cols+1, 2)
A388982sq(row, col) = if(1==row, A388980(col), my(f = factor(A388980(col))); for(i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])+(row-1))); factorback(f));
A388982list(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] = A388982sq(col, (a-(col-1))))); (v); };
v388982 = A388982list(up_to);
A388982(n) = v388982[n];

Crossrefs

Cf. A003961, A007913, A229125, A246278, A388980 (topmost row).

Cf. also A228058 (all terms are included once in this array).

Sequence in context: A394507 A262027 A328487 * A083003 A364130 A278117

Adjacent sequences: A388979 A388980 A388981 * A388983 A388984 A388985

Keyword

nonn,tabl

Author

Antti Karttunen, Sep 22 2025

Status

approved