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A125624 Array read by antidiagonals: n-th row contains the positive integers with their largest prime factor equal to the n-th 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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
This sequence is a permutation of the integers >= 2.
Since the table has been entered by rising 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
Start with table headed by primes in the first row, then list beneath each prime(k) the ordered prime(k)-smooth numbers. Read the table by falling antidiagonals to get the terms of this sequence. - David James Sycamore, Jun 23 2024
LINKS
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][c-1]) && 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 A366948 A297440
KEYWORD
nonn,tabl
AUTHOR
Leroy Quet, Jan 27 2007
EXTENSIONS
Extended by Ray Chandler, Feb 09 2007
STATUS
approved

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Last modified July 25 03:44 EDT 2024. Contains 374586 sequences. (Running on oeis4.)