A337199 -id:A337199 - cp's OEIS frontend

A337198 Number of distinct prime factors in A337194(n) = 1+A000265(sigma(n)), where A000265(k) gives the odd part of k.

1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1

Offset: 1

Antti Karttunen, Aug 20 2020

nonn

The first 3 occurs at a(137).

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences related to sigma(n)

Cf. A000203, A000265, A001221, A161942, A336698, A337194.

Cf. also A058062, A336691, A337199.

A000265(n) = (n>>valuation(n,2));
A337198(n) = (omega(1+A000265(sigma(n))));

a(n) = A001221(A337194(n)) = 1 + A001221(A336698(n)).

A337200 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(A337194(i)) = A278222(A337194(j)), for all i, j >= 1.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 3, 3, 4, 5, 1, 3, 1, 1, 1, 5, 4, 1, 1, 3, 1, 1, 1, 2, 1, 6, 3, 1, 1, 6, 5, 1, 4, 5, 3, 3, 1, 1, 6, 7, 3, 5, 2, 1, 3, 1, 4, 6, 1, 5, 1, 1, 2, 1, 5, 3, 3, 1, 1, 3, 3, 5, 5, 6, 1, 3, 1, 5, 4, 7, 7, 1, 5, 1, 2, 3, 1, 6, 6, 8, 1, 5, 1, 3, 1, 1, 5, 9, 3, 10, 5, 2, 2, 9, 1

Offset: 1

Antti Karttunen, Aug 20 2020

nonn

Restricted growth sequence transform of f(n) = A278222(A337194(n)).

For all i, j: A324400(i) = A324400(j) => a(i) = a(j) => A337199(i) = A337199(j).

Cf. A000203, A000265, A278222, A161942, A336698, A337194, A337199.

Cf. also A286622, A324400, A337201.

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; };
A000265(n) = (n>>valuation(n, 2));
A337194(n) = (1+A000265(sigma(n)));
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A278222(n) = A046523(A005940(1+n));
v337200 = rgs_transform(vector(up_to, n, A278222(A337194(n))));
A337200(n) = v337200[n];

cp's OEIS Frontend

A337198 Number of distinct prime factors in A337194(n) = 1+A000265(sigma(n)), where A000265(k) gives the odd part of k.

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