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

1,2

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

Table of n, a(n) for n=1..74.

Index entries for sequences computed from indices in prime factorization

Prog

(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));

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).

Sequence in context: A259315 A211771 A211772 * A231573 A327204 A047409

Adjacent sequences: A353352 A353353 A353354 * A353356 A353357 A353358

Keyword

nonn

Author

Antti Karttunen and Peter Munn, Apr 15 2022

Status

approved