A353357 Numbers k for which A353328(k) < A353329(k). Positions of -1's in A353354.

3, 7, 13, 19, 21, 24, 29, 37, 39, 42, 43, 53, 56, 57, 61, 71, 78, 79, 81, 87, 89, 91, 101, 104, 105, 107, 111, 113, 114, 129, 131, 133, 139, 151, 152, 159, 163, 168, 173, 174, 181, 182, 183, 189, 192, 193, 195, 199, 203, 213, 222, 223, 229, 231, 232, 237, 239, 247, 251, 258, 259, 263, 266, 267, 271, 281, 285, 293

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 A353356.

Crossrefs

Cf. A000005, A003961, A048675, A332823, A353328, A353329, A353354, A353355, A353356.

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));
isA353357(n) = (0>A353354(n));

PARI

A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
isA353357(n) = (1==((numdiv(n)*A048675(n))%3));

Formula

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