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 A294897 a(n) = Product_{d|n, gcd(d,n/d)>1} prime(A101296(gcd(d,n/d))-1). 6
 1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 4, 1, 1, 1, 12, 1, 4, 1, 4, 1, 1, 1, 16, 2, 1, 4, 4, 1, 1, 1, 36, 1, 1, 1, 80, 1, 1, 1, 16, 1, 1, 1, 4, 4, 1, 1, 144, 2, 4, 1, 4, 1, 16, 1, 16, 1, 1, 1, 16, 1, 1, 4, 252, 1, 1, 1, 4, 1, 1, 1, 1600, 1, 1, 4, 4, 1, 1, 1, 144, 12, 1, 1, 16, 1, 1, 1, 16, 1, 16, 1, 4, 1, 1, 1, 1296, 1, 4, 4, 80, 1, 1, 1, 16, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Antti Karttunen, Table of n, a(n) for n = 1..16384 FORMULA a(n) = Product_{d|n} A008578(A101296(gcd(d,n/d))). For n >= 1, A001222(a(n)) = A048105(n). PROG (PARI) up_to = 16384 rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om, invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om, invec[i], i); outvec[i] = u; u++ )); outvec; }; A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ This function from Charles R Greathouse IV, Aug 17 2011 v101296 = rgs_transform(vector(up_to, n, A046523(n))); A101296(n) = v101296[n]; A294897(n) = { my(m=1); fordiv(n, d, if(gcd(d, n/d)>1, m *= prime(A101296(gcd(d, n/d))-1))); m; }; CROSSREFS Cf. A005117 (the positions of ones). Cf. A101296, A294895. Cf. also A292258 (A292259), A293515, A294875 for similar filter sequences. Sequence in context: A292589 A297404 A235388 * A252733 A181876 A131505 Adjacent sequences:  A294894 A294895 A294896 * A294898 A294899 A294900 KEYWORD nonn AUTHOR Antti Karttunen, Nov 21 2017 STATUS approved

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Last modified September 21 02:41 EDT 2020. Contains 337266 sequences. (Running on oeis4.)