A346529 a(n) is the number of primes that are nearest neighbors of the n-th Ramanujan's highly composite number A002182.

1, 1, 2, 2, 2, 1, 1, 1, 2, 0, 2, 2, 1, 1, 1, 1, 0, 1, 1, 2, 1, 1, 1, 0, 0, 1, 0, 2, 0, 2, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 2, 0, 0, 0

Offset

1,3

Comments

Terms are only 0, 1 or 2.

Links

Table of n, a(n) for n=1..87.

Formula

a(n) = A010051(A002182(n)-1) + A010051(A002182(n)+1). - Michel Marcus, Aug 17 2021

Example

For n = 8 the 8th highly composite numbers is 48, thus its nearest neighbors are 47 and 49, only 47 is prime so a(8) = 1.
For n = 9 the 9th highly composite numbers is 60, thus its nearest neighbors are 59 and 61, both are twin primes so a(9) = 2.
For n = 10 the 10th highly composite numbers is 120, thus its nearest neighbors are 119 and 121, both are nonprimes so a(10) = 0.

Mathematica

f[n_] := Count[n + {-1, 1}, _?PrimeQ]; s = {}; dm = 0; Do[d = DivisorSigma[0, n]; If[d > dm, dm = d; AppendTo[s, f[n]]], {n, 1, 10^6}]; s (* Amiram Eldar, Aug 17 2021 *)

Crossrefs

Cf. A001097, A002182, A010051, A018252, A068507, A340580.

Sequence in context: A199840 A126067 A327490 * A238408 A048858 A246465

Adjacent sequences: A346526 A346527 A346528 * A346530 A346531 A346532

Keyword

nonn

Author

Omar E. Pol, Aug 17 2021

Extensions

More terms from Amiram Eldar, Aug 17 2021

Status

approved