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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 (list; graph; refs; listen; history; text; internal format)
 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 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 A233438 Adjacent sequences:  A331662 A331663 A331664 * A331666 A331667 A331668 KEYWORD nonn AUTHOR Amiram Eldar, Jan 23 2020 STATUS approved

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Last modified October 22 13:15 EDT 2021. Contains 348170 sequences. (Running on oeis4.)