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A295657
Multiplicative with a(p^e) = p^floor((e-1)/2).
3
1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 2, 1
OFFSET
1,8
LINKS
FORMULA
a(1) = 1; for n > 1, a(n) = A020639(n)^A004526(A067029(n)-1) * a(A028234(n)).
a(n) = A000188(A003557(n)).
a(n) = 1 iff A212793(n) = 1.
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 15/Pi^2 = 1.519817... (A082020). - Amiram Eldar, Nov 30 2022
MATHEMATICA
Array[Apply[Times, FactorInteger[#] /. {p_, e_} /; p > 0 :> p^Floor[(e - 1)/2]] &, 105] (* Michael De Vlieger, Nov 28 2017 *)
PROG
(Scheme, with memoization-macro definec) (definec (A295657 n) (if (= 1 n) 1 (* (expt (A020639 n) (A004526 (- (A067029 n) 1))) (A295657 (A028234 n)))))
(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^floor((f[i, 2]-1)/2)); } \\ Amiram Eldar, Nov 30 2022
CROSSREFS
Cf. A004709 (positions of ones), A082020, A212793.
Cf. also A008834, A053150, A061704.
Sequence in context: A325988 A328856 A053150 * A163379 A006466 A316439
KEYWORD
nonn,mult
AUTHOR
Antti Karttunen, Nov 28 2017
STATUS
approved