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

Author

Ilya Gutkovskiy, Oct 31 2020

Keywords

• nonn
• easy

Examples

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

Links

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

Crossrefs

Cf. A001227, A047983, A334655, A335097.

Programs

Mathematica

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

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

Formula

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