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A371090
Additive with a(p^1) = 1, a(p^e) = a(A276086(e)) for e > 1, where A276086 is the primorial base exp-function.
3
0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 2, 2, 1, 2, 2, 3, 1, 3, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 3, 2, 3, 2, 2, 1, 3, 1, 2, 2, 1, 2, 3, 1, 2, 2, 3, 1, 3, 1, 2, 2, 2, 2, 3, 1, 2, 1, 2, 1, 3, 2, 2, 2, 3, 1, 3, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 1, 3, 1, 3, 3, 2, 1, 3, 1, 3, 2, 2, 1, 3, 2, 2, 2, 2, 2, 4, 1, 2, 2, 2, 2, 3, 1, 2
OFFSET
1,6
COMMENTS
Used to construct A371091.
FORMULA
Additive with a(p^1) = 1, a(p^e) = A371091(e) for e > 1.
For all n >= 1, A001221(n) <= a(n) <= A001222(n).
PROG
(PARI)
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A371090(n) = vecsum(apply(e->if(1==e, 1, A371090(A276086(e))), factor(n)[, 2]));
CROSSREFS
Differs from A064547 for the first time at n=63, where a(64) = 1, while A064547(64) = 2.
Differs from A058061 for the first time at n=128, where a(128) = 2, while A058061(128) = 3.
Sequence in context: A305832 A058061 A376886 * A064547 A318306 A345935
KEYWORD
nonn
AUTHOR
Antti Karttunen, Mar 31 2024
STATUS
approved