A305899 Filter sequence related to factorization ("prime") signatures of Stern polynomials when factored over Z.
1, 2, 2, 3, 2, 4, 2, 5, 3, 4, 2, 6, 2, 4, 4, 7, 2, 6, 2, 6, 4, 4, 2, 8, 2, 4, 5, 6, 2, 9, 2, 10, 4, 4, 4, 11, 2, 4, 4, 8, 2, 9, 2, 6, 6, 4, 2, 12, 3, 4, 4, 6, 2, 8, 2, 8, 4, 4, 2, 13, 2, 4, 9, 14, 2, 9, 2, 6, 4, 9, 2, 15, 2, 4, 6, 6, 2, 9, 2, 12, 4, 4, 2, 13, 4, 4, 4, 8, 2, 13, 2, 6, 4, 4, 2, 16, 2, 6, 6, 6, 2, 9, 2, 8, 9
Offset: 1
Keywords
Links
- Antti Karttunen, Table of n, a(n) for n = 1..65537
Programs
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PARI
up_to = 65537; 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; }; pfps(n) = { my(f=factor(n)); sum(i=1, #f~, f[i, 2] * 'x^(primepi(f[i, 1])-1)); }; A284010(n) = { if(!bitand(n, (n-1)), 0, my(p=0, f=vecsort(factor(pfps(n))[, 2], ,4)); prod(i=1, #f, (p=nextprime(p+1))^f[i])); } A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From Michel Marcus A260443(n) = if(n<2, n+1, if(n%2, A260443(n\2)*A260443(n\2+1), A003961(A260443(n\2)))); A284011(n) = A284010(A260443(n)); v305899 = rgs_transform(vector(up_to, n, A284011(n))); A305899(n) = v305899[n];
Comments