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A284318
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Triangle read by rows in which row n lists divisors d of n such that n divides d^n.
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5
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1, 2, 3, 2, 4, 5, 6, 7, 2, 4, 8, 3, 9, 10, 11, 6, 12, 13, 14, 15, 2, 4, 8, 16, 17, 6, 18, 19, 10, 20, 21, 22, 23, 6, 12, 24, 5, 25, 26, 3, 9, 27, 14, 28, 29, 30, 31, 2, 4, 8, 16, 32, 33, 34, 35, 6, 12, 18, 36, 37, 38, 39, 10, 20, 40, 41, 42, 43, 22, 44, 15, 45, 46, 47, 6, 12, 24, 48, 7, 49, 10, 50
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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EXAMPLE
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Triangle begins:
1;
2;
3;
2, 4;
5;
6;
7;
2, 4, 8;
3, 9;
10;
11;
6, 12;
13;
14;
15;
2, 4, 8, 16.
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MAPLE
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f:= proc(n) local r;
r:= convert(numtheory:-factorset(n), `*`);
op(sort(convert(map(`*`, numtheory:-divisors(n/r), r), list)))
end proc:
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MATHEMATICA
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Flatten[Table[Select[Range[n], Divisible[n, #] && Divisible[#^n, n] &], {n, 50}]] (* Indranil Ghosh, Mar 25 2017 *)
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PROG
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(Magma) [[u: u in [1..n] | Denominator(n/u) eq 1 and Denominator(u^n/n) eq 1]: n in [1..50]];
(PARI) for(n=1, 50, for(i=1, n, if(n%i==0 & (i^n)%n==0, print1(i, ", "); ); ); print(); ); \\ Indranil Ghosh, Mar 25 2017
(Python)
for n in range(1, 51):
....print [i for i in range(1, n + 1) if n%i==0 and (i**n)%n==0] # Indranil Ghosh, Mar 25 2017
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CROSSREFS
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Cf. A000961 (1 together with k such that k divides p^k for some prime divisor p of k), A005361 (row length), A007774 (m such that m divides s^m for some semiprime divisor s of m), A007947 (smallest u such that u^n|n and n|u, or divisor k such that A000005(k) = 2^A001221(n)), A057723 (row sums), A066503 (difference between largest x and smallest y such that x^n|n, n|x, y^n|n and n|y).
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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