A293221 a(n) = Product_{d|n, dA019565(A289813(d)); a product obtained from the 1-digits present in ternary expansions of proper divisors of n.

1, 2, 2, 2, 2, 6, 2, 12, 6, 6, 2, 36, 2, 4, 18, 12, 2, 30, 2, 360, 12, 10, 2, 540, 6, 60, 30, 360, 2, 900, 2, 120, 30, 10, 12, 2700, 2, 4, 180, 360, 2, 540, 2, 360, 450, 6, 2, 5400, 4, 120, 30, 360, 2, 210, 30, 5040, 12, 14, 2, 1701000, 2, 84, 180, 2520, 180, 1260, 2, 840, 18, 12600, 2, 94500, 2, 140, 180, 840, 20, 18900, 2, 756000, 210, 210, 2, 23814000, 30

Offset: 1

Author

Antti Karttunen, Oct 03 2017

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 1..6561

Crossrefs

Cf. A019565, A289813, A293214, A293222, A293223 (restricted growth sequence transform), A293226.

Cf. also A290091.

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
A289813(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==1, 1, 0)), 2); } \\ From Remy Sigrist
A293221(n) = { my(m=1); fordiv(n,d,if(d < n,m *= A019565(A289813(d)))); m; };

Formula

a(n) = Product_{d|n, dA019565(A289813(d)).

For all n >= 0, a(3^n) = A002110(n).