A317490 a(n) = min {i - j} where i*j is a factorization of the n-th partial product of the semiprimes (A112141).

0, 2, 6, 3, 12, 3, 126, 153, 765, 1050, 5348, 14850, 85050, 501200, 91280, 3661983, 25633881, 66271296, 215467945, 254861640, 5311480020, 75327142968, 122703152000, 2187956957004, 3449084839200, 19305922856220, 11327171375520, 58038845751810, 2222926571960640

Offset

1,2

Links

Table of n, a(n) for n=1..29.

Example

a(1) =   0 since the first semiprime is    4 =    2 *    2;
a(2) =   2 since 4*6               =      24 =    4 *    6;
a(3) =   6 since 4*6*9             =     216 =   12 *   18;
a(4) =   3 since 4*6*9*10          =    2160 =   45 *   48;
a(5) =  12 since 4*6*9*10*14       =   30240 =  168 *  180;
a(6) =   3 since 4*6*9*10*14*15    =  453600 =  172 *  175;
a(7) = 126 since 4*6*9*10*14*15*21 = 9525600 = 3024 * 3150; etc.

Mathematica

SemiPrimePi[n_] := Sum[PrimePi[n/Prime[i]] - i + 1, {i, PrimePi[Sqrt[n]]}]; SemiPrime[n_] := Block[{e = Floor[Log[2, n] + 1], a, b}, a = 2^e; Do[b = 2^p; While[SemiPrimePi@a < n, a = a + b]; a = a - b/2, {p, e, 0, -1}]; a + b/2]; a[n_] := Block[{sp = Times @@ Array[SemiPrime@# &, n], d}, d = DivisorSigma[0, sp]/2; -Subtract @@  Take[ Divisors@ sp, {d, d + 1}]]; a[1] = 0; Array[a, 29]

Crossrefs

Inspired by A003681, and analogous to A061057 and A061060.

Cf. A112141.

Sequence in context: A322365 A297553 A347558 * A256466 A303771 A298480

Adjacent sequences: A317487 A317488 A317489 * A317491 A317492 A317493

Keyword

nonn

Author

Robert G. Wilson v, Jul 29 2018

Status

approved