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proposed

<a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

Cf. also A286621, A331299.

Antti Karttunen, <a href="/A331280/b331280.txt">Table of n, a(n) for n = 1..65537</a>

allocated Lexicographically earliest infinite sequence such that a(i) = a(j) => A278220(i) = A278220(j) for Antti Karttunenall i, j.

1, 2, 3, 2, 4, 3, 5, 2, 6, 4, 7, 3, 8, 5, 9, 2, 10, 6, 11, 4, 12, 7, 13, 3, 9, 8, 6, 5, 14, 9, 15, 2, 16, 10, 17, 6, 18, 11, 19, 4, 20, 12, 21, 7, 9, 13, 22, 3, 12, 9, 23, 8, 24, 6, 25, 5, 26, 14, 27, 9, 28, 15, 12, 2, 29, 16, 30, 10, 31, 17, 32, 6, 33, 18, 34, 11, 25, 19, 35, 4, 6, 20, 36, 12, 37, 21, 38, 7, 39, 9, 40, 13, 41, 22, 42, 3, 43, 12, 16, 9, 44, 23, 45, 8, 46

1,2

Restricted growth sequence transform of A278220(n) (= A046523(A241909(n))).

(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; };

A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ This function from A046523

A241909(n) = if(1==n||isprime(n), 2^primepi(n), my(f=factor(n), h=1, i, m=1, p=1, k=1); while(k<=#f~, p = nextprime(1+p); i = primepi(f[k, 1]); m *= p^(i-h); h = i; if(f[k, 2]>1, f[k, 2]--, k++)); (p*m));

A278220(n) = A046523(A241909(n));

v331280 = rgs_transform(vector(up_to, n, A278220(n)));

A331280(n) = v331280[n];

Cf. A046523, A241909, A278220.

Cf. also A286621.

allocated

nonn

Antti Karttunen, Jan 17 2020

approved

editing

allocated for Antti Karttunen

allocated

approved