A388981 Square array A(n,k), read by descending antidiagonals, where A(1, k) = A388984(k), and for n > 1, A(n, k) = A003961(A(n-1), k).

12, 18, 45, 20, 75, 175, 28, 63, 245, 539, 44, 99, 275, 847, 1573, 48, 117, 325, 637, 1859, 2873, 50, 405, 425, 833, 2057, 3757, 5491, 52, 147, 4375, 931, 2299, 3211, 6137, 8303, 68, 153, 605, 26411, 2783, 3887, 6647, 10051, 15341, 72, 171, 475, 1183, 190333, 4901, 8381, 10469, 19343, 26071, 76, 675, 575, 1127, 3179, 485537, 8959, 11191, 16399, 27869, 35557

Offset

1,1

Comments

This is otherwise like the primeshift array A246278, but includes only those columns of it that contain non-powers of primes (A024619) that are of the form p * m^2, where p is prime and m > 1, i.e., numbers k such that A007913(k) is a prime and A001221(k) > 1.

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, A388984(k)/2).

Example

The top left corner of the array:
k= |    1      2      3      4      5         6      7      8       9        10
---+----------------------------------------------------------------------------
1  |   12,    18,    20,    28,    44,       48,    50,    52,     68,       72,
2  |   45,    75,    63,    99,   117,      405,   147,   153,    171,      675,
3  |  175,   245,   275,   325,   425,     4375,   605,   475,    575,     6125,
4  |  539,   847,   637,   833,   931,    26411,  1183,  1127,   1421,    41503,
5  | 1573,  1859,  2057,  2299,  2783,   190333,  3179,  3509,   3751,   224939,
6  | 2873,  3757,  3211,  3887,  4901,   485537,  4693,  5239,   6253,   634933,
7  | 5491,  6137,  6647,  8381,  8959,  1586899,  8993, 10693,  11849,  1773593,

Prog

(PARI)
up_to_cols = 210;
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));
A388981list(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] = A388981sq(col, (a-(col-1))))); (v); };
v388981 = A388981list(up_to);
A388981(n) = v388981[n];

Crossrefs

Permutation of A388983.

Cf. A003961, A007913, A024619, A246278, A388984 (topmost row).

Otherwise like array A388982, but without any columns containing prime powers only.

Derived arrays, the applied function is given in parentheses: A388987 (A326127), A388988 (A326128), A388989 (A388991), A388990 (A388992), A388993 (A007913), A389168 (A388978), A389169 (A388979).

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

Sequence in context: A133403 A152615 A258088 * A259263 A341039 A279369

Adjacent sequences: A388978 A388979 A388980 * A388982 A388983 A388984

Keyword

nonn,tabl

Author

Antti Karttunen, Sep 22 2025

Status

approved