A178313 Absolute difference between prime factors of n-th semiprime mod n.

0, 1, 0, 3, 0, 2, 4, 1, 0, 1, 8, 3, 2, 3, 10, 5, 0, 14, 6, 16, 6, 7, 8, 20, 10, 4, 12, 12, 12, 26, 6, 28, 12, 14, 16, 34, 18, 19, 10, 0, 18, 38, 40, 12, 20, 44, 22, 2, 24, 21, 26, 25, 50, 16, 26, 0, 56, 29, 58, 32, 6, 33, 1, 35, 22, 36, 34, 8, 68, 35, 38, 24, 34, 70, 4, 35, 42, 76, 6, 0

Offset

1,4

Links

Alois P. Heinz, Table of n, a(n) for n = 1..20000

Example

a(2)=1 because semiprime(2) = 6 = 3*2 and (3-2) mod 2 = 1.

Mathematica

semiPrimeQ[n_] := Plus @@ Last /@ FactorInteger@ n == 2; f[n_] := Subtract @@ Reverse@ Flatten[ Table[ #[[1]], {#[[2]]}] & /@ FactorInteger@ n]; t = Select[ Range@ 215, semiPrimeQ]; Table[ Mod[ f[ t[[n]]], n], {n, 80}]
f[{a_, b_}]:=Module[{c=FactorInteger[b][[;; , 1]]}, If[Length[c]==1, 0, Mod[Differences[c][[1]], a]]]; Module[{nn=300, spr}, spr=Select[Range[nn], PrimeOmega[#]==2&]; f/@Thread[{Range[ Length[ spr]], spr}]] (* Harvey P. Dale, May 29 2024 *)

Crossrefs

Cf. A001358, A178102, A109313.

Sequence in context: A112974 A113069 A136163 * A190013 A171088 A058624

Adjacent sequences: A178310 A178311 A178312 * A178314 A178315 A178316

Keyword

nonn

Author

Juri-Stepan Gerasimov, Dec 20 2010

Status

approved