A095301 Numbers n such that there is some k < n with n*sigma(k) = k*sigma(n).

28, 140, 200, 224, 234, 270, 308, 364, 476, 496, 532, 600, 644, 672, 700, 812, 819, 868, 936, 1036, 1148, 1170, 1204, 1316, 1400, 1484, 1488, 1540, 1638, 1652, 1708, 1800, 1820, 1876, 1988, 2016, 2044, 2200, 2212, 2324, 2380, 2464, 2480, 2492, 2574, 2600

Offset: 1

Author

Klaus Brockhaus, Jun 01 2004

Keywords

• nonn

Comments

Original name: Numbers n such that A094759(n) < n.

Agrees with A050973 without duplicates.

Also numbers n such that the value sigma(n)/n has already been reached before n. If n belongs to the sequence then A214701(n) = A214701(n-1). - Michel Marcus, Aug 19 2012

Examples

			A094759(28) = 6 < 28, hence 28 is in the sequence.
		

References

• B. Spearman and K. S. Williams, Handbook of Estimates in the Theory of Numbers, Carleton Math. Lecture Note Series No. 14, 1975; see p. 3.2, Eq. (3.9).

Links

• Michel Marcus and Donovan Johnson, Table of n, a(n) for n = 1..10000 (first 180 terms from Michel Marcus)
• P. Erdős, Remarks on number theory II: Some problems on the sigma function, Acta Arith., 5 (1959), 171-177.

Crossrefs

Cf. A000203, A094759, A050973.

Programs

PARI

for(n=1,2600,s=sigma(n);k=1;while(n*sigma(k)!=k*s,k++);if(k
				

PARI

allab = []; nb = 0; for (i=1, n, ab = sigma(i)/i; already = 0; if (length(allab) > 0, for (j=1, length(allab), if (ab == allab[j], already = 1; break););); if (already == 1,  nb++; print1(i, ","), allab = concat(allab, ab););)
/* Michel Marcus, Aug 19 2012 */

Extensions

New name from Charles R Greathouse IV, Jul 21 2015