A337557 Number of integers less than n with the same number of odd divisors as n.

0, 1, 0, 2, 1, 2, 3, 3, 0, 4, 5, 6, 7, 8, 0, 4, 9, 1, 10, 11, 1, 12, 13, 14, 2, 15, 2, 16, 17, 3, 18, 5, 4, 19, 5, 3, 20, 21, 6, 22, 23, 7, 24, 25, 0, 26, 27, 28, 4, 5, 8, 29, 30, 9, 10, 31, 11, 32, 33, 12, 34, 35, 1, 6, 13, 14, 36, 37, 15, 16, 38, 6, 39, 40, 2, 41, 17, 18, 42, 43

Offset

1,4

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Formula

a(n) = |{j < n : A001227(j) = A001227(n)}|.

Example

a(10) = 4 because A001227(10) = 2 and also A001227(3) = A001227(5) = A001227(6) = A001227(7) = 2.

Mathematica

Table[Length[Select[Range[n - 1], Sum[Mod[d, 2], {d, Divisors[#]}] == Sum[Mod[d, 2], {d, Divisors[n]}] &]], {n, 80}]

Prog

(PARI) a(n)={my(t=numdiv(n/2^valuation(n, 2))); sum(k=1, n-1, numdiv(k/2^valuation(k, 2))==t)} \\ Andrew Howroyd, Oct 31 2020
(PARI) first(n) = { my(m = Map(), res = vector(n)); for(i = 1, n, q = numdiv(i >> valuation(i, 2)); if(mapisdefined(m, q), res[i] = mapget(m, q); mapput(m, q, res[i]+1); , mapput(m, q, 1) ) ); res } \\ David A. Corneth, Oct 31 2020

Crossrefs

Cf. A001227, A047983, A334655, A335097.

Sequence in context: A054758 A077876 A095056 * A186333 A272917 A239627

Adjacent sequences: A337554 A337555 A337556 * A337558 A337559 A337560

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Oct 31 2020

Status

approved