A346100 -id:A346100 - cp's OEIS frontend

A346090 Numbers k such that k and A346098(k) are relatively prime; positions of ones in A346099, positions of zeros in A346100.

1, 8, 9, 16, 18, 25, 36, 40, 42, 45, 48, 49, 50, 60, 63, 70, 77, 80, 81, 84, 90, 91, 96, 98, 100, 115, 117, 119, 120, 125, 126, 128, 133, 135, 140, 144, 147, 150, 154, 160, 161, 162, 165, 168, 169, 170, 180, 192, 195, 196, 209, 220, 221, 228, 230, 234, 238, 242, 250, 255, 256, 259, 260, 266, 270, 273, 288, 294, 297, 308, 315

Offset: 1

Antti Karttunen, Jul 07 2021

nonn

Positions of ones in A346099, positions of zeros in A346100.

A346099 a(n) = gcd(n, A346098(n)).

Original entry on oeis.org

1, 2, 3, 4, 5, 3, 7, 1, 1, 5, 11, 3, 13, 7, 5, 1, 17, 1, 19, 5, 7, 11, 23, 3, 1, 13, 3, 7, 29, 5, 31, 2, 11, 17, 7, 1, 37, 19, 13, 1, 41, 1, 43, 11, 1, 23, 47, 1, 1, 1, 17, 13, 53, 9, 11, 7, 19, 29, 59, 1, 61, 31, 1, 4, 13, 11, 67, 17, 23, 1, 71, 3, 73, 37, 25, 19, 1, 13, 79, 1, 1, 41, 83, 1, 17, 43, 29, 11, 89

Offset: 1

Antti Karttunen, Jul 07 2021

nonn

Only powers of primes (A000961) occur as terms. A346100 lists the exponents.

Cf. A000961, A064989, A319626, A324886, A346095, A346096, A346097, A346098, A346100.

Cf. A346090 (positions of ones).

A064989(n) = { my(f = factor(n)); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
A319626(n) = (n / gcd(n, A064989(n)));
A346099(n) = gcd(n, A064989(A319626(A324886(n)))); \\ Rest of program in A324886.

a(n) = gcd(n, A346098(n)) = gcd(n, A064989(A319626(A324886(n)))).

A346087 a(n) = min(A071178(n), A329348(n)).

Original entry on oeis.org

0, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3

Offset: 1

Antti Karttunen, Jul 07 2021

nonn

Each term of A345941 is a power of the greatest prime factor of n, a(n) is the exponent of that term: a(n) = A100995(A345941(n)).

Values 0..5 occur for the first time at n = 1, 2, 4, 108, 324, 9375.

Cf. A006530, A100995, A071178, A324886, A329044, A329348, A345941, A346100.

A345941(n) = gcd(n,A329044(n));
A346087(n) = isprimepower(A345941(n)); \\ Rest of program given in A329044.

a(n) = min(A071178(n), A329348(n)).
a(n) = A100995(A345941(n)).
For all n >= 1, A006530(n)^a(n) = A345941(n).

cp's OEIS Frontend

A346090 Numbers k such that k and A346098(k) are relatively prime; positions of ones in A346099, positions of zeros in A346100.

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A346099 a(n) = gcd(n, A346098(n)).

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A346087 a(n) = min(A071178(n), A329348(n)).

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