A275337 Least k such that sigma(k*n) = sigma(k*n+1), or 0 if no such k exists.

14, 7, 319, 341, 537

Offset: 1

Author

Altug Alkan, Jul 24 2016

Keywords

• nonn
• more

Comments

Terms 6 through 30, with 0 signifying no such k <= 10^6: {0, 2, 220708, 1649, 23039, 87, 0, 6141, 1, 179, 110354, 873, 0, 86, 0, 5813, 62, 58, 0, 37497, 17149, 699, 0, 33, 0}. - Michael De Vlieger, Jul 25 2016

a(28) = 16806458, from A002961 b-file. - Michel Marcus, Jul 26 2016

If a(n) = 0, then a(m*n) = 0 for all m > 0. If c is a divisor of a(n), then a(c*n) = a(n)/c. - Chai Wah Wu, Jul 26 2016

Examples

			a(3) = 319 because sigma(319*3) = sigma(319*3+1) = 1440.
		

Links

• Michel Marcus, Some terms

Crossrefs

Cf. A002961.

Programs

Mathematica

Table[SelectFirst[Range[10^6], DivisorSigma[1, # n] == DivisorSigma[1, # n + 1] &], {n, 30}] /. k_ /; MissingQ@ k -> 0 (* Michael De Vlieger, Jul 25 2016, Version 10.2 *)

PARI

a(n) = {my(k = 1); while (sigma(k*n) != sigma(k*n+1), k++); k;} \\ Michel Marcus, Jul 26 2016