A344883 -id:A344883 - cp's OEIS frontend

A344881 Numbers such that A011772(k) > A011772(d) for all their proper divisors d.

1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 19, 20, 22, 23, 25, 27, 29, 30, 31, 32, 33, 35, 37, 38, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 56, 59, 61, 62, 63, 64, 65, 67, 69, 70, 71, 72, 73, 76, 77, 79, 80, 81, 83, 84, 85, 86, 87, 89, 90, 91, 94, 95, 97, 99, 101, 102, 103, 104, 107, 108, 109, 110

Offset: 1

Antti Karttunen, Jun 01 2021

nonn

Union of A000961 and A344883.
Complement of A344882.
Positions of 1's in A344590, in A344759, and in A344880 (characteristic function).

A344980 Numbers k such that A011772(k) does not divide A344875(k).

Original entry on oeis.org

12, 14, 15, 20, 22, 30, 33, 35, 38, 42, 44, 45, 46, 48, 51, 52, 54, 56, 60, 62, 63, 65, 66, 69, 70, 72, 76, 77, 80, 84, 85, 86, 87, 88, 90, 91, 92, 94, 95, 99, 102, 104, 105, 108, 110, 112, 114, 115, 116, 117, 118, 119, 123, 124, 126, 130, 132, 133, 134, 135, 138, 140, 141, 142, 143, 144, 145, 148, 152, 153, 154, 156

Offset: 1

Antti Karttunen, Jun 05 2021

nonn

The first term not in A344883 is 60. First terms included in A344883, but not here are: 900, 1260, 1560, 3740, 6552, 6669, etc. (A344694). See also comments in A344975.

Cf. A011772, A344694, A344875, A344975.

Complement of A344974. Positions of nonzero terms in A344973, and of terms > 1 in A344970.

A011772(n) = { if(n==1, return(1)); my(f=factor(if(n%2, n, 2*n)), step=vecmax(vector(#f~, i, f[i, 1]^f[i, 2]))); forstep(m=step, 2*n, step, if(m*(m-1)/2%n==0, return(m-1)); if(m*(m+1)/2%n==0, return(m))); }; \\ From A011772
A344875(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^(f[2, i]+(2==f[1, i]))-1)); };
isA344980(n) = (A344875(n)%A011772(n));

cp's OEIS Frontend

A344881 Numbers such that A011772(k) > A011772(d) for all their proper divisors d.

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A344980 Numbers k such that A011772(k) does not divide A344875(k).

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