A324395 a(n) = A017666(A005940(1+n)), where A005940 is the Doudna sequence and A017666(n) = n/gcd(n,sigma(n)).

1, 2, 3, 4, 5, 1, 9, 8, 7, 5, 5, 3, 25, 6, 27, 16, 11, 7, 21, 10, 35, 5, 15, 2, 49, 50, 75, 36, 125, 9, 81, 32, 13, 11, 11, 1, 55, 7, 63, 4, 77, 35, 35, 5, 175, 5, 9, 12, 121, 98, 49, 100, 245, 25, 225, 24, 343, 125, 125, 27, 625, 54, 243, 64, 17, 13, 39, 11, 65, 11, 33, 7, 13, 55, 55, 3, 275, 21, 189, 40, 143, 77, 77, 5, 385, 35, 105, 1, 539

Offset: 0

Author

Antti Karttunen, Mar 05 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16500
• Antti Karttunen, Data supplement: n, a(n) computed for n = 0..65537
• Index entries for sequences related to binary expansion of n
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A005940, A017666, A324054, A324055, A324058, A324349, A324394.

Programs

PARI

A324395(n) = { my(m1=1,m2=1,p=2,mp=p*p); while(n, if(!(n%2), p=nextprime(1+p); mp = p*p, m1 *= p; if(3==(n%4),mp *= p,m2 *= (mp-1)/(p-1))); n>>=1); m1/gcd(m1,m2); };

PARI

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
A017666(n) = (n/gcd(n, sigma(n)));
A324395(n) = A017666(A005940(1+n));

Formula

a(n) = A017666(A005940(1+n)) = A005940(1+n) / A324394(n).