A331665 Numbers k with a record number of divisors d < sqrt(k) such that d + k/d is prime.

1, 2, 6, 30, 210, 2310, 3570, 4830, 11550, 30030, 43890, 111930, 131670, 510510, 690690, 870870, 1021020, 2459730, 9699690, 13123110, 17160990, 40750710, 146006070, 223092870, 340510170, 358888530, 688677990, 1462190730, 2445553110, 2911018110, 6469693230

Offset

1,2

Comments

The corresponding record values are 0, 1, 2, 4, 8, 12, 13, 14, 15, 21, 24, 25, 29, 40, 41, 46, 49, 51, 70, 77, 88, 89, 90, 117, 120, 147, 153, 154, 155, 161, 263, ...

Apparently all the primorial numbers (A002110) are terms. The record values of terms that are primorial numbers are terms of A103787.

Links

Table of n, a(n) for n=1..31.

Example

2 has one divisor below sqrt(2), 1, such that 1 + 2/1 = 3 is prime.
6 has 2 divisors below sqrt(6), 1 and 2, such that 1 + 6/1 = 7 and 2 + 6/2 = 5 are primes.
30 has 4 divisors below sqrt(30), 1, 2, 3, and 5 such that 1 + 30/1 = 31, 2 + 30/2 = 17, 3 + 30/3 = 13 and 5 + 30/5 = 11 are primes.

Mathematica

divCount[n_] := DivisorSum[n, Boole @ PrimeQ[# + n/#] &, #^2 < n &]; seq = {}; dm = -1; Do[d1 = divCount[n]; If[d1 > dm, dm = d1; AppendTo[seq, n]], {n, 1, 10^6}]; seq

Crossrefs

Cf. A002110, A093890, A103787, A161510.

Sequence in context: A068215 A305400 A096775 * A171989 A335069 A361807

Adjacent sequences: A331662 A331663 A331664 * A331666 A331667 A331668

Keyword

nonn

Author

Amiram Eldar, Jan 23 2020

Status

approved