A340362 -id:A340362 - cp's OEIS frontend

A340364 a(n) = gcd(A005940(n), A324106(n)), where A324106(n) is multiplicative with a(p^e) = A005940(p^e).

1, 2, 3, 4, 5, 6, 9, 8, 7, 10, 15, 12, 25, 18, 3, 16, 11, 14, 21, 20, 1, 30, 45, 24, 49, 50, 75, 36, 125, 6, 81, 32, 1, 22, 3, 28, 55, 42, 3, 40, 77, 2, 105, 60, 35, 90, 135, 48, 121, 98, 3, 100, 245, 150, 75, 72, 7, 250, 375, 12, 625, 162, 9, 64, 1, 2, 39, 44, 5, 6, 99, 56, 91, 110, 3, 84, 5, 6, 189, 80, 143, 154, 231

Offset: 1

Antti Karttunen, Jan 06 2021

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16384

Cf. A005940, A324106, A340362, A340365, A340366.

Cf. also A339969.

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
A324106(n) = { my(f=factor(n)); prod(i=1, #f~, A005940(f[i,1]^f[i,2])); };
A340364(n) = gcd(A005940(n), A324106(n));

a(n) = gcd(A005940(n), A324106(n)) = gcd(A005940(n), A340362(n)).

A340365 a(n) = A005940(n) / gcd(A005940(n), A324106(n)), where A324106(n) is multiplicative with a(p^e) = A005940(p^e).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 1, 35, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 1, 13, 1, 11, 1, 1, 1, 21, 1, 1, 35, 1, 1, 5, 1, 1, 1, 1, 1, 49, 1, 1, 1, 3, 1, 49, 1, 1, 9, 1, 1, 27, 1, 17, 13, 1, 1, 13, 11, 1, 1, 1, 1, 55, 1, 55, 21, 1, 1, 1, 1, 1, 35, 7, 1, 21, 1, 1, 5, 7, 1, 875, 1, 27, 1, 1, 1, 121

Offset: 1

Antti Karttunen, Jan 06 2021

nonn

It is conjectured that A070776 gives the positions of all ones after the initial one. If that holds, then for all i, j: a(i) = a(j) => A340363(i) = A340363(j).

Antti Karttunen, Table of n, a(n) for n = 1..16384

Cf. A005940, A070776, A324106, A340362, A340364, A340366.

Cf. also A305800, A340363.

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A324106(n) = { my(f=factor(n)); prod(i=1, #f~, A005940(f[i,1]^f[i,2])); };
A340365(n) = { my(t=A005940(n)); t / gcd(t, A324106(n)); };

a(n) = A005940(n) / A340364(n) = A005940(n) / gcd(A005940(n), A324106(n)).

cp's OEIS Frontend

A340364 a(n) = gcd(A005940(n), A324106(n)), where A324106(n) is multiplicative with a(p^e) = A005940(p^e).

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