A353356 Numbers k for which A353328(k) > A353329(k). Positions of 1's in A353354.

2, 5, 10, 11, 16, 17, 22, 23, 30, 31, 34, 40, 41, 46, 47, 54, 55, 59, 62, 66, 67, 70, 73, 80, 82, 83, 85, 88, 94, 97, 102, 103, 109, 115, 118, 127, 128, 130, 134, 135, 136, 137, 138, 146, 149, 154, 155, 157, 165, 166, 167, 176, 179, 184, 186, 187, 190, 191, 194, 197, 205, 206, 211, 218, 227, 233, 235, 238, 240, 241

Offset: 1

Author

Antti Karttunen and Peter Munn, Apr 15 2022

Keywords

• nonn

Comments

For any term k present here, A003961(k) is present in A353357.

Links

• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000005, A003961, A048675, A332823, A353328, A353329, A353354, A353355, A353357.

Programs

PARI

A332823(n) = { my(f = factor(n),u=(sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2)%3); if(2==u,-1,u); };
A353354(n) = sumdiv(n,d,A332823(d));
isA353356(n) = (0<A353354(n));

PARI

A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
isA353356(n) = (2==((numdiv(n)*A048675(n))%3));

Formula

{a(n) : n >= 1} = {m : tau(m) * A048675(m) == 2 (mod 3)}, where tau is the number of divisors function, A000005.