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A284318 Triangle read by rows in which row n lists divisors d of n such that n divides d^n. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n lists divisors of n that are divisible by A007947(n). - Robert Israel, Apr 27 2017

LINKS

Robert Israel, Table of n, a(n) for n = 1..10002  (rows 1 to 5250, flattened)

FORMULA

T(n,k) = A007947(n) * A027750(A003557(n), k). - Robert Israel, Apr 27 2017

EXAMPLE

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.

MAPLE

f:= proc(n) local r;

    r:= convert(numtheory:-factorset(n), `*`);

    op(sort(convert(map(`*`, numtheory:-divisors(n/r), r), list)))

end proc:

map(f, [$1..100]); # Robert Israel, Apr 27 2017

MATHEMATICA

Flatten[Table[Select[Range[n], Divisible[n, #] && Divisible[#^n, n] &], {n, 50}]] (* Indranil Ghosh, Mar 25 2017 *)

PROG

(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 xrange(1, 51):

....print [i for i in xrange(1, n + 1) if n%i==0 and (i**n)%n==0] # Indranil Ghosh, Mar 25 2017

CROSSREFS

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).

Cf. A003557, A027750.

Sequence in context: A227842 A304731 A304728 * A322791 A304745 A176789

Adjacent sequences:  A284315 A284316 A284317 * A284319 A284320 A284321

KEYWORD

nonn,tabf

AUTHOR

Juri-Stepan Gerasimov, Mar 25 2017

STATUS

approved

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Last modified February 21 01:15 EST 2019. Contains 320364 sequences. (Running on oeis4.)