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A331665
Numbers k with a record number of divisors d < sqrt(k) such that d + k/d is prime.
0
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.
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jan 23 2020
STATUS
approved