The On-Line Encyclopedia of Integer Sequences (OEIS)

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A249917

Square array read by antidiagonals where the n-th row lists the integers x such that gcd(x, sigma(x)) = n.
(history; published version)

#10 by Bruno Berselli at Thu Aug 01 03:48:01 EDT 2019

STATUS

proposed

approved

#9 by Jon E. Schoenfield at Thu Aug 01 03:40:49 EDT 2019

STATUS

editing

proposed

#8 by Jon E. Schoenfield at Thu Aug 01 03:40:46 EDT 2019

NAME

Square array read by antidiagonals where the n-th row lists the integers x such that GCDgcd(x, sigma(x)) = n.

EXAMPLE

1, 2, 3, 4, 5, 7, 8, ...

10, 14, 20, 22, 26, 34, 38, ...

15, 18, 33, 45, 51, 69, 72, ...

12, 44, 48, 76, 88, 92, 108, ...

95, 145, 200, 295, 395, 445, 475, ...

6, 30, 42, 54, 66, 78, 102, ...

91, 196, 273, 287, 455, 581, 637, ...

56, 112, 184, 248, 368, 376, 432, ...

...

CROSSREFS

Cf. A009194 (GCDgcd(n, sigma(n))), A014567 (GCDgcd(n, sigma(n))=1), A074391 (smallest x such that GCDgcd(x, sigma(x)) is n),

STATUS

approved

editing

#7 by N. J. A. Sloane at Sat Jan 17 19:43:29 EST 2015

STATUS

proposed

approved

#6 by Michel Marcus at Wed Jan 14 01:22:06 EST 2015

STATUS

editing

proposed

#5 by Michel Marcus at Wed Jan 14 01:13:38 EST 2015

NAME

allocated for Michel MarcusSquare array read by antidiagonals where the n-th row lists the integers x such that GCD(x, sigma(x)) = n.

DATA

1, 2, 10, 3, 14, 15, 4, 20, 18, 12, 5, 22, 33, 44, 95, 7, 26, 45, 48, 145, 6, 8, 34, 51, 76, 200, 30, 91, 9, 38, 69, 88, 295, 42, 196, 56, 11, 46, 72, 92, 395, 54, 273, 112, 153, 13, 52, 87, 108, 445, 66, 287, 184, 288, 40, 16, 58, 99, 124, 475, 78, 455, 248, 459, 190, 473

OFFSET

1,2

COMMENTS

First line is A014567 and first column is A074391.

This is a permutation of the positive integers.

LINKS

<a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

EXAMPLE

Array begins:

1, 2, 3, 4, 5, 7, 8, ...

10, 14, 20, 22, 26, 34, 38, ...

15, 18, 33, 45, 51, 69, 72, ...

12, 44, 48, 76, 88, 92, 108, ...

95, 145, 200, 295, 395, 445, 475, ...

6, 30, 42, 54, 66, 78, 102, ...

91, 196, 273, 287, 455, 581, 637, ...

56, 112, 184, 248, 368, 376, 432, ...

...

PROG

(PARI) triangle(nn) = {v = vector(nn); for (n=1, nn, for (k=1, n, if (! v[k], x = 1, x = v[k] + 1); while (gcd(sigma(x), x) != k, x++); print1(x, ", "); v[k] = x; ); print(); ); }

CROSSREFS

Cf. A009194 (GCD(n, sigma(n))), A014567 (GCD(n, sigma(n))=1), A074391 (smallest x such that GCD(x, sigma(x)) is n),

KEYWORD

allocated

nonn,tabl

AUTHOR

Michel Marcus, Jan 14 2015

STATUS

approved

editing

#4 by Michel Marcus at Wed Jan 14 01:13:38 EST 2015

NAME

allocated for Michel Marcus

KEYWORD

recycled

allocated

#3 by R. J. Mathar at Fri Jan 09 14:35:31 EST 2015

STATUS

editing

approved

#2 by R. J. Mathar at Fri Jan 09 14:35:28 EST 2015

NAME

allocated for José María Grau Ribas

KEYWORD

allocated

recycled

STATUS

approved

editing

#1 by José María Grau Ribas at Sat Nov 08 15:08:15 EST 2014

NAME

allocated for José María Grau Ribas

KEYWORD

allocated

STATUS

approved