A293443 Multiplicative with a(p^e) = A019565(A193231(e)).

1, 2, 2, 6, 2, 4, 2, 3, 6, 4, 2, 12, 2, 4, 4, 10, 2, 12, 2, 12, 4, 4, 2, 6, 6, 4, 3, 12, 2, 8, 2, 5, 4, 4, 4, 36, 2, 4, 4, 6, 2, 8, 2, 12, 12, 4, 2, 20, 6, 12, 4, 12, 2, 6, 4, 6, 4, 4, 2, 24, 2, 4, 12, 15, 4, 8, 2, 12, 4, 8, 2, 18, 2, 4, 12, 12, 4, 8, 2, 20, 10, 4, 2, 24, 4, 4, 4, 6, 2, 24, 4, 12, 4, 4, 4, 10, 2, 12, 12, 36, 2, 8, 2, 6, 8

Offset: 1

Author

Antti Karttunen, Oct 31 2017

Keywords

• nonn
• mult

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from exponents in factorization of n

Crossrefs

Cf. A019565, A028234, A067029, A193231.

Cf. also A270428, A293442, A293231, A293439.

Programs

PARI

A019565(n) = {my(j,v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ This function from M. F. Hasler
A193231(n) = { my(x='x); subst(lift(Mod(1, 2)*subst(Pol(binary(n), x), x, 1+x)), x, 2) }; \\ And this from Franklin T. Adams-Watters
vecproduct(v) = { my(m=1); for(i=1,#v,m *= v[i]); m; };
A293443(n) = vecproduct(apply(e -> A019565(A193231(e)), factorint(n)[, 2]));

Scheme

;; With memoization-macro definec.
(definec (A293443 n) (if (= 1 n) n (* (A019565 (A193231 (A067029 n))) (A293443 (A028234 n)))))

Formula

a(1) = 1; for n > 1, a(n) = A019565(A193231(A067029(n))) * a(A028234(n)).

For all n >= 1, A007814(a(n)) = A293439(n).

For all k in A270428, A007814(a(k)) = A001221(k).