A284004 - OEIS

%I #12 Mar 19 2017 01:10:42

%S 1,2,6,2,30,6,2,6,210,30,6,30,2,6,30,6,2310,210,30,210,6,30,210,30,2,

%T 6,30,6,210,30,6,30,30030,2310,210,2310,30,210,2310,210,6,30,210,30,

%U 2310,210,30,210,2,6,30,6,210,30,6,30,2310,210,30,210,6,30,210,30,510510,30030,2310,30030,210,2310,30030,2310,30,210,2310,210,30030,2310,210,2310

%N a(n) = A046523(A284003(n)).

%H Antti Karttunen, <a href="/A284004/b284004.txt">Table of n, a(n) for n = 0..8191</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%F a(n) = A046523(A284003(n)).

%F a(n) = A002110(A001222(A284003(n))) = A002110(A209281(n))). [Latter so far only conjectured.]

%t Table[Times @@ MapIndexed[Prime[First@ #2]^#1 &, Reverse@ Sort@ FactorInteger[#][[All, -1]]] - Boole[# == 1] &@ Apply[Times, FactorInteger[#] /. {p_, e_} /; e > 0 :> Times @@ (p^Mod[e, 2])] &[Times @@ Map[#1^#2 & @@ # &, FactorInteger[#] /. {p_, e_} /; e == 1 :> {Times @@ Prime@ Range@ PrimePi@ p, e}] &[Times @@ Prime@ Flatten@ Position[#, 1] &@ Reverse@ IntegerDigits[n, 2]]], {n, 0, 52}] (* _Michael De Vlieger_, Mar 18 2017 *)

%o (PARI)

%o \\ Code for A284003 given under that entry.

%o A046523(n) = my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]) \\ From _Charles R Greathouse IV_, Aug 17 2011

%o A284004(n) = A046523(A284003(n));

%o (Scheme) (define (A284004 n) (A046523 (A284003 n)))

%Y Cf. A001222, A002110, A046523, A209281, A284003.

%K nonn

%O 0,2

%A _Antti Karttunen_, Mar 18 2017