

A270433


a(n) = number of terms A270431 <= n; least monotonic left inverse of A270431.


5



0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 3, 3, 3, 4, 5, 5, 5, 6, 7, 7, 8, 9, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 14, 14, 15, 16, 17, 18, 19, 19, 19, 19, 20, 20, 20, 21, 22, 23, 24, 24, 25, 26, 27, 27, 28, 28, 28, 29, 30, 30, 30, 31, 32, 33, 34, 34, 34, 35, 35, 36, 37, 37, 37, 37, 38, 39, 39, 40, 41, 42
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OFFSET

1,7


LINKS

Antti Karttunen, Table of n, a(n) for n = 1..35000


FORMULA

a(1) = 0, for n > 1, a(n) = (A048673(n)A064216(n) reduced modulo 2)) + a(n1).
Other identities. For all n >= 1:
a(n) = n  A270432(n).
a(A270431(n)) = n.


MATHEMATICA

f[n_] := (Times @@ Power[If[# == 1, 1, NextPrime@ #] & /@ First@ #, Last@ #] + 1)/2 &@ Transpose@ FactorInteger@ n; g[n_] := Times @@ Power[If[# == 1, 1, NextPrime[#, 1]] & /@ First@ #, Last@ #] &@ Transpose@ FactorInteger[2 n  1]; s = Select[Range@ 200, Xor[EvenQ@ f@ #, EvenQ@ g@ #] &] ; Table[Count[s, k_ /; k <= n], {n, 88}] (* Michael De Vlieger, Mar 17 2016 *)


PROG

(Scheme, with memoizationmacro definec)
(definec (A270433 n) (if (<= n 1) 0 (+ (modulo ( (A048673 n) (A064216 n)) 2) (A270433 ( n 1)))))


CROSSREFS

Cf. A048673, A064216, A270431, A270432, A270434.
Sequence in context: A025775 A169993 A325620 * A169994 A169995 A213419
Adjacent sequences: A270430 A270431 A270432 * A270434 A270435 A270436


KEYWORD

nonn


AUTHOR

Antti Karttunen, Mar 17 2016


STATUS

approved



