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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
OFFSET
1,4
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. also A292258 (A292259), A293515, A294875 for similar filter sequences.
Sequence in context: A292589 A297404 A235388 * A252733 A181876 A131505
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 21 2017
STATUS
approved