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A278165 Least number with the prime signature of the n-th Jacobsthal number.

%I A278165 #27 May 21 2017 06:39:13
%S A278165 1,1,2,2,2,6,2,6,12,6,2,210,2,6,30,30,2,420,2,420,30,30,2,30030,30,6,
%T A278165 120,2310,6,30030,2,210,210,6,210,19399380,6,6,30,60060,6,60060,2,
%U A278165 30030,4620,30,6,223092870,6,30030,2310,30030,6,120120,420,510510,210,2310,30,401120980260,2,6,4620,30030,2310,9699690,6,30030,210,9699690,6,14841476269620,6
%N A278165 Least number with the prime signature of the n-th Jacobsthal number.
%H A278165 Antti Karttunen (terms 1..257) & Hans Havermann, <a href="/A278165/b278165.txt">Table of n, a(n) for n = 1..1032</a>
%F A278165 a(n) = A046523(A001045(n)).
%t A278165 Table[Times @@ MapIndexed[(Prime@ First@ #2)^#1 &, #] &@ If[Length@# == 1 && #[[1, 1]] == 1, {0}, Reverse@ Sort@ #[[All, -1]]] &@ FactorInteger[ (2^n - (-1)^n)/3], {n, 120}] (* _Michael De Vlieger_, Nov 21 2016 *)
%o A278165 (PARI)
%o A278165 A001045(n) = (2^n - (-1)^n) / 3;
%o A278165 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 A278165 A278165(n) = A046523(A001045(n));
%o A278165 for(n=1, 257, write("b278165.txt", n, " ", A278165(n)));
%o A278165 (Scheme) (define (A278165 n) (A046523 (A001045 n)))
%Y A278165 Cf. A001045, A046523.
%Y A278165 Cf. A107036 (positions of 2's), A286565 (rgs-version of this sequence).
%Y A278165 Cf. also A278245, A278248, A278258, A286567.
%K A278165 nonn
%O A278165 1,3
%A A278165 _Antti Karttunen_, Nov 19 2016