A342463 a(n) = A342001(A342456(n)); "wild part" of the arithmetic derivative of A342456(n).

1, 1, 1, 2, 1, 2, 12, 8, 1, 2, 6, 4, 50, 24, 16, 16, 1, 2, 6, 4, 126, 62, 46, 26, 1486, 100, 1142, 48, 2056, 32, 342, 10, 1, 2, 6, 4, 94, 24, 72, 18, 242, 120, 1588, 54, 3408, 92, 1740, 22, 6846, 2972, 4340, 766, 5048, 1374, 652, 376, 71156, 22710, 20390, 64, 738580, 4272, 568, 20, 1, 2, 6, 4, 264, 12, 196, 8, 318

Offset

0,4

Comments

Like in A342462, also here the subsequences starting at each n = 2^k seem to be slowly converging towards A329886: 1, 2, 6, 4, 30, 12, 36, 8, 210, 60, ...

Links

Antti Karttunen, Table of n, a(n) for n = 0..8192

Index entries for sequences related to binary expansion of n

Index entries for sequences related to primorial base

Formula

a(n) = A342001(A342456(n)) = A342002(A329886(n)) = A342920(A005940(1+n)).

Mathematica

Block[{a, f, r = MixedRadix[Reverse@ Prime@ Range@ 24]}, f[n_] := Times @@ MapIndexed[Prime[First[#2]]^#1 &, Reverse@ IntegerDigits[n, r]]; a[0] = 1; a[1] = 2; a[n_] := a[n] = If[EvenQ@ n, (Times @@ Map[Prime[PrimePi@ #1 + 1]^#2 & @@ # &, FactorInteger[#]] - Boole[# == 1])*2^IntegerExponent[#, 2] &[a[n/2]], 2 a[(n - 1)/2]]; Array[#1/#2 & @@ {If[# < 2, 0, # Total[#2/#1 & @@@ FactorInteger[#]]] &@ Abs[#], #/Times @@ FactorInteger[#][[All, 1]]} &@ f@ a[#] &, 73, 0]] (* Michael De Vlieger, Mar 17 2021 *)

Prog

(PARI)
\\ Needs also code from A342456.
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003557(n) = (n/factorback(factorint(n)[, 1]));
A342001(n) = (A003415(n) / A003557(n));
A342463(n) = A342001(A342456(n));

Crossrefs

Cf. A003415, A003557, A005940, A108951, A329886, A342001, A342002, A342456, A342462, A342920.

Sequence in context: A324121 A320834 A355932 * A052579 A266314 A153908

Adjacent sequences: A342460 A342461 A342462 * A342464 A342465 A342466

Keyword

nonn,look

Author

Antti Karttunen, Mar 15 2021

Status

approved