A275233 Least k such that k and k + n have same average of divisors.

5, 33, 11, 11, 17, 26, 13, 19, 29, 23, 55, 23, 17, 141, 47, 38, 85, 38, 23, 46, 39, 47, 71, 41, 29, 177, 29, 59, 89, 47, 65, 53, 101, 212, 107, 59, 41, 182, 115, 83, 91, 182, 62, 71, 141, 119, 235, 71, 53, 115, 158, 107, 265, 79, 41, 89, 53, 47, 123, 83, 143, 58, 117, 106, 197

Offset

1,1

Comments

Least k such that A000203(n+k) / A000005(n+k) = A000203(k) / A000005(k).

Records are a(1) = 5, a(2) = 33, a(11) = 55, a(14) = 141, a(26) = 177, a(34) = 212, a(47) = 235, a(53) = 265, a(93) = 285, a(98) = 366, a(102) = 442, a(107) = 535, a(158) = 902, a(166) = 2739, a(758) = 3424, a(863) = 4315, a(866) = 4470, a(1171) = 5855, a(1478) = 6790, a(1493) = 7465, a(1823) = 9115, a(2203) = 11015, a(3463) = 14795, a(3833) = 19165, a(6459) = 19379, a(6865) = 20257, a(7926) = 22918, a(9938) = 23161, .... - Charles R Greathouse IV, Jul 21 2016

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

a(1) = 5 because sigma(5) / tau(5) = (1 + 5) / 2 = 3 and sigma(6) / tau(6) = (1 + 2 + 3 + 6) / 4 = 3.

Prog

(PARI) avdiv(n)=my(f=factor(n)); sigma(f)/numdiv(f)
a(n)=my(k=1); while(avdiv(k) != avdiv(k+n), k++); k \\ Charles R Greathouse IV, Jul 21 2016

Crossrefs

Cf. A000005, A000203, A003601.

Sequence in context: A203112 A349099 A174471 * A359971 A043068 A194405

Adjacent sequences: A275230 A275231 A275232 * A275234 A275235 A275236

Keyword

nonn

Author

Altug Alkan, Jul 20 2016

Status

approved