A353355 Numbers k for which A353328(k) is equal to A353329(k).

1, 4, 6, 8, 9, 12, 14, 15, 18, 20, 25, 26, 27, 28, 32, 33, 35, 36, 38, 44, 45, 48, 49, 50, 51, 52, 58, 60, 63, 64, 65, 68, 69, 72, 74, 75, 76, 77, 84, 86, 90, 92, 93, 95, 96, 98, 99, 100, 106, 108, 110, 112, 116, 117, 119, 120, 121, 122, 123, 124, 125, 126, 132, 140, 141, 142, 143, 144, 145, 147, 148, 150, 153, 156

Offset: 1

Author

Antti Karttunen and Peter Munn, Apr 15 2022

Keywords

• nonn

Comments

Numbers k such that A353354(k) [= Sum_{d|k} A332823(d)] is zero.

If k is present, then A003961(k), A348717(k) and (for all m >= 1) k*m^3 are present also.

Includes all numbers whose number of divisors is a multiple of 3 (A059269). Each number in A059269 has its divisors equally distributed between the classes defined by A332823; and they are exactly the numbers, m, for which A353354(m) = A353446(m) = 0.

Links

• Index entries for sequences computed from indices in prime factorization

Crossrefs

Positions of 0's in A353354.

Union of A059269 and A332820.

A353356, A353357 and this sequence partition the natural numbers to three disjoint sets, based on the values obtained by A353354.

Cf. A003961, A048675, A332823, A348717, A353328, A353329, A353352, A353354, A353380 (characteristic function), A353382, A353414, A353446.

Cf. A000578, A001248, A059269 (subsequences).

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));
isA353355(n) = (0==A353354(n));