A331598 - OEIS

A331598

a(n) = A122111(n) / gcd(A122111(n),A241909(n)).

1, 1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 2, 1, 8, 1, 1, 1, 1, 1, 4, 2, 16, 1, 2, 9, 32, 5, 8, 1, 2, 1, 1, 4, 64, 3, 3, 1, 128, 8, 4, 1, 4, 1, 16, 1, 256, 1, 2, 27, 1, 16, 32, 1, 5, 1, 8, 32, 512, 1, 6, 1, 1024, 2, 1, 2, 8, 1, 64, 64, 2, 1, 3, 1, 2048, 5, 128, 9, 16, 1, 4, 7, 4096, 1, 12, 4, 8192, 128, 16, 1, 10, 3, 256, 256, 16384, 8, 2, 1, 1, 4, 9, 1, 32, 1, 32, 1 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,6`
	COMMENTS	`It appears that these and the terms of A331599 have the same prime signatures, that is, A046523(a(n)) = A046523(A331599(n)) seems to hold for all n. However, the sequences are not equivalence-class-wise same: a(6) = a(12) = 2, whereas A331599(6) = 3 and A331599(12) = 5.`
	LINKS	`Antti Karttunen, Table of n, a(n) for n = 1..10000` `Index entries for sequences computed from indices in prime factorization`
	FORMULA	`a(n) = A122111(n)/A331598(n) = A122111(n) / gcd(A122111(n),A241909(n)).` `a(n) = A331599(A241916(n)).`
	MATHEMATICA	Array[If[# == 1, 1, #1/GCD[#1, #2] & @@ {Block[{k = #, m = 0}, Times @@ Power @@@ Table[k -= m; k = DeleteCases[k, 0]; {Prime@ Length@ k, m = Min@ k}, Length@ Union@ k]] &@ Catenate[ConstantArray[PrimePi[#1], #2] & @@@ #], Function[t, Times @@ Prime@ Accumulate[If[Length@ t < 2, {0}, Join[{1}, ConstantArray[0, Length@t - 2], {-1}]] + ReplacePart[t, Map[#1 -> #2 & @@ # &, #]]]]@ ConstantArray[0, Transpose[#][[1, -1]]] &[# /. {p_, e_} /; p > 0 :> {PrimePi@ p, e}]} &@ FactorInteger[#]] &, 90] (* Michael De Vlieger, Jan 25 2020, after JungHwan Min at A122111 *)
	PROG	`(PARI) A331598(n) = { my(u=A122111(n)); u/gcd(u, A241909(n)); };`
	CROSSREFS	`Cf. A122111, A241909, A241916, A331594, A331595, A331599.` `Sequence in context: A160449 A326322 A089940 * A123974 A238350 A355754` `Adjacent sequences: A331595 A331596 A331597 * A331599 A331600 A331601`
	KEYWORD	`nonn`
	AUTHOR	`Antti Karttunen, Jan 22 2020`
	STATUS	`approved`