A394361 Numbers k such that the values of d(k^2+1) set records, where d(k) is the number of divisors of k (A000005).

1, 3, 7, 13, 43, 47, 157, 307, 993, 2163, 3957, 5257, 17557, 18543, 66347, 191407, 565807, 617427, 1413443, 1732593, 2457057, 8360893, 16485763, 36484843, 51853693, 162166243, 599832943

Offset

1,2

Comments

No prime factor of a(n)^2 + 1 is of the form 4*k + 3. - David A. Corneth, Mar 19 2026

a(28) <= 2280635557. - David A. Corneth, Mar 21 2026

Links

Table of n, a(n) for n=1..27.

Example

993 is in this sequence because 993^2 + 1 = 986050 which has 48 divisors, and there is no number k between 1 and 992 where k^2 + 1 has >= 48 divisors.

Prog

(PARI) print1(r=1); for(n=3, 1e5, if(numdiv(n^2+1)>r, r=numdiv(n^2+1); print1(", "n)))

Crossrefs

Cf. A000005, A002182, A002522, A008784, A193432, A394612.

Sequence in context: A147447 A062605 A191974 * A174241 A289556 A086208

Adjacent sequences: A394358 A394359 A394360 * A394362 A394363 A394364

Keyword

nonn,more

Author

Zhicheng Wei, Mar 17 2026

Status

approved