

A125624


Array read by antidiagonals: nth row contains the positive integers with their largest prime factor equal to the nth prime.


8



2, 3, 4, 5, 6, 8, 7, 10, 9, 16, 11, 14, 15, 12, 32, 13, 22, 21, 20, 18, 64, 17, 26, 33, 28, 25, 24, 128, 19, 34, 39, 44, 35, 30, 27, 256, 23, 38, 51, 52, 55, 42, 40, 36, 512, 29, 46, 57, 68, 65, 66, 49, 45, 48, 1024, 31, 58, 69, 76, 85, 78, 77, 56, 50, 54, 2048, 37, 62, 87, 92
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OFFSET

1,1


COMMENTS

This sequence is a permutation of the integers >= 2.
Since the table has been entered by raising instead of falling antidiagonals, the sequence represents the transpose, with columns instead of rows: cf. the "table" link, section "infinite square array".  M. F. Hasler, Oct 22 2019


LINKS

Ivan Neretin, Table of n, a(n) for n = 1..5050


EXAMPLE

Array begins: (rows here appear as columns in the "table" display of the sequence)
2, 4, 8, 16, 32, 64, 128, 256, 512, ... (A000079)
3, 6, 9, 12, 18, 24, 27, 36, 48, ... (A065119)
5, 10, 15, 20, 25, 30, 40, 45, 50, ... (A080193)
7, 14, 21, 28, 35, 42, 49, 56, 63, ... (A080194)
11, 22, 33, 44, 55, 66, 77, 88, 99, ... (A080195)
13, 26, 39, 52, 65, 78, 91, 104, 117, ... (A080196)
The 3rd row, for example, contains the positive integers where the 3rd prime, 5, is the largest prime divisor. That is, each integer in this row is divisible by 5 and may be divisible by 2 or 3 as well, but none of the integers in this row are divisible by primes larger than 5. (So for example, 35 = 5*7 is excluded from the 3rd row.)


MATHEMATICA

lpf[n_] := FactorInteger[n][[ 1, 1]]; f[n_, m_] := f[n, m] = Block[{k}, k = If[m == 1, Prime[n], f[n, m  1] + 1]; While[lpf[k] != Prime[n], k++ ]; k]; Table[f[ d  m + 1, m], {d, 12}, {m, d}] // Flatten (* Ray Chandler, Feb 09 2007 *)


PROG

(PARI) T=List(); r=c=1; for(n=1, 99, #T<r && listput(T, List(prime(r))); #T[r]<c && listput(T[r], T[r][c1]) && while(vecmax(factor(T[r][c]+=T[r][1])[, 1])>T[r][1], ); print1(T[r][c]", "); r && c++  r=c+c=1) \\ M. F. Hasler, Oct 22 2019


CROSSREFS

Cf. A083140, A006530, A000040 (1st col), A033286 (main diag), A077320.
Sequence in context: A185974 A129129 A114622 * A262388 A297440 A232895
Adjacent sequences: A125621 A125622 A125623 * A125625 A125626 A125627


KEYWORD

nonn,tabl


AUTHOR

Leroy Quet, Jan 27 2007


EXTENSIONS

Extended by Ray Chandler, Feb 09 2007


STATUS

approved



