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A317490
a(n) = min {i - j} where i*j is a factorization of the n-th partial product of the semiprimes (A112141).
0
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
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
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Jul 29 2018
STATUS
approved