login
A295658
Multiplicative with a(p^e) = p^max(0,(floor(e/2)-1)).
3
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1
OFFSET
1,16
COMMENTS
a(n) differs from A053164(n) = A000188(A000188(n)) for the first time at n=64, where a(64) = 4, while A053164(64) = 2.
LINKS
FORMULA
a(1) = 1; for n > 1, a(n) = A020639(n)^max(0,A004526(A067029(n))-1) * a(A028234(n)).
a(n) = A003557(A000188(n)).
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = zeta(3)/zeta(6) = 1.181564... (A157289). - Amiram Eldar, Nov 30 2022
EXAMPLE
For n = 64 = 2^6, a(64) = 2^(floor(6/2)-1) = 2^2 = 4.
MATHEMATICA
f[p_, e_] := p^Max[0, Floor[e/2-1]]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Nov 30 2022 *)
PROG
(Scheme, with memoization-macro definec) (definec (A295658 n) (if (= 1 n) 1 (* (expt (A020639 n) (max 0 (+ -1 (A004526 (A067029 n))))) (A295658 (A028234 n)))))
(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^max(0, floor(f[i, 2]/2-1))); } \\ Amiram Eldar, Nov 30 2022
CROSSREFS
Cf. A046100 (positions of ones), A157289.
Sequence in context: A063775 A053164 A365333 * A307427 A318672 A359910
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, Nov 28 2017
STATUS
approved