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A294873
a(n) = Product_{d|n, d>1, d = x^(2k-1) for some maximal k >= 1} prime(k).
5
1, 2, 2, 2, 2, 8, 2, 6, 2, 8, 2, 16, 2, 8, 8, 6, 2, 16, 2, 16, 8, 8, 2, 96, 2, 8, 6, 16, 2, 128, 2, 30, 8, 8, 8, 32, 2, 8, 8, 96, 2, 128, 2, 16, 16, 8, 2, 192, 2, 16, 8, 16, 2, 96, 8, 96, 8, 8, 2, 1024, 2, 8, 16, 30, 8, 128, 2, 16, 8, 128, 2, 384, 2, 8, 16, 16, 8, 128, 2, 192, 6, 8, 2, 1024, 8, 8, 8, 96, 2, 1024, 8, 16, 8, 8, 8, 1920, 2, 16, 16, 32, 2, 128, 2
OFFSET
1,2
FORMULA
a(n) = Product_{d|n, d>1, r = A052409(d) is odd} A000040((r+1)/2).
Other identities. For all n >= 1:
A001222(a(n)) = A056595(n).
A007814(a(n)) = A183096(n).
PROG
(PARI) A294873(n) = { my(m=1, e); fordiv(n, d, if(d>1, e = ispower(d); if(!e, m += m, if((e>1)&&(e%2), m *= prime((e+1)/2))))); m; };
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 11 2017
STATUS
approved