A324058 -id:A324058 - cp's OEIS frontend

A336476 a(n) = gcd(A000593(n), A336475(n)).

1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 12, 1, 2, 1, 2, 2, 4, 2, 2, 2, 1, 2, 4, 2, 2, 12, 2, 1, 12, 2, 4, 1, 2, 2, 4, 2, 2, 4, 2, 2, 6, 2, 2, 2, 3, 1, 12, 2, 2, 4, 4, 2, 4, 2, 2, 12, 2, 2, 2, 1, 4, 12, 2, 2, 12, 4, 2, 1, 2, 2, 2, 2, 4, 4, 2, 2, 1, 2, 2, 4, 4, 2, 12, 2, 2, 6, 28, 2, 4, 2, 20, 2, 2, 3, 6, 1, 2, 12, 2, 2, 24

Offset: 1

Antti Karttunen, Jul 30 2020

nonn

All odd terms k in A001599 (Ore's Harmonic numbers) satisfy a(k) = A336475(k).

Antti Karttunen, Table of n, a(n) for n = 1..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Cf. A000265, A000593, A001227, A001599, A324121, A336475.

Cf. also A324058, A336320.

A000593(n) = sigma(n>>valuation(n, 2));
A336475(n) = { my(f=factor(n)); prod(i=1, #f~, if(2==f[i,1],1,(1+f[i,2]) * (f[i,1]^f[i,2]))); };
A336476(n) = gcd(A000593(n), A336475(n));

a(n) = gcd(A000593(n), A336475(n)).

a(n) = A324121(A000265(n)).

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

Original entry on oeis.org

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

Antti Karttunen, Mar 05 2019

nonn

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)

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

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); };

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));

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

cp's OEIS Frontend

A336476 a(n) = gcd(A000593(n), A336475(n)).

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

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