A060676 Numbers k such that sigma (x) = k has exactly 12 solutions.

1512, 1872, 2352, 3192, 3780, 4104, 4560, 4752, 5880, 6120, 8160, 8424, 8820, 11424, 13056, 15264, 16464, 16704, 17160, 17360, 17760, 18648, 19680, 19800, 20880, 22752, 23616, 24552, 24864, 27432, 30336, 30492, 31200, 32448, 35328

Offset: 1

Author

Robert G. Wilson v, Apr 18 2001

Keywords

• nonn

Examples

			1512 = sigma(480) = sigma(636) = sigma(736) = sigma(748) = sigma(830) = sigma(902) = sigma(1006) = sigma(1105) = sigma(1255) = sigma(1391) = sigma(1411) = sigma(1511).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems (invphi.gp).

Crossrefs

Cf. A000203.

Number of solutions: A007369 (0), A007370 (1), A007371 (2), A007372 (3), A060660 (4), A060661 (5), A060662 (6), A060663 (7), A060664 (8), A060665 (9), A060666 (10), A060678 (11), this sequence (12).

Programs

Mathematica

a = Table[ 0, {50000} ]; Do[ s = DivisorSigma[ 1, n ]; If[ s < 50001, a[ [ s ] ]++ ], {n, 1, 50000} ]; Select[ Range[ 50000 ], a[ [ # ] ] == 12 & ]
Take[Sort[Transpose[Select[Tally[DivisorSigma[1,Range[100000]]],#[[2]] == 12&]][[1]]],50] (* Harvey P. Dale, Jan 18 2013 *)

PARI

is(k) = invsigmaNum(k) == 12 \\ Amiram Eldar, Nov 18 2024, using Max Alekseyev's invphi.gp