A344315 a(n) is the least number k such that A048105(k) = A048105(k+1) = 2*n, and 0 if it does not exist.

1, 27, 135, 2511, 2295, 6975, 5264, 12393728, 12375, 2200933376, 108224, 257499, 170624, 3684603215871, 4402431, 2035980763136, 126224, 41680575, 701443071, 46977524, 1245375, 2707370000, 4388175, 3129761024, 1890944

Offset

0,2

Comments

There are no two consecutive numbers with an odd number of non-unitary divisors, since A048105(k) is odd only if k is a perfect square.

a(25) <= 1965640805422351777791, a(26) <= 3127059999. In general, a(n) <= A215199(n+1). - Daniel Suteu, May 20 2021

Links

Table of n, a(n) for n=0..24.

Example

a(0) = 1 since A048105(1) = A048105(2) = 0.
a(1) = 27 since A048105(27) = A048105(28) = 2.

Mathematica

nd[n_] := DivisorSigma[0, n] - 2^PrimeNu[n]; seq[max_] := Module[{s = Table[0, {max}], k = 2, c = 0, nd1 = 0}, While[c < max, If[(nd2 = nd[k]) == nd1 && nd2 < 2*max && s[[nd2/2 + 1]] == 0, c++; s[[nd2/2 + 1]] = k - 1]; nd1 = nd2; k++]; s]; seq[7]

Prog

(PARI)
A048105(n) = numdiv(n) - 2^omega(n);
isok(n, k) = A048105(k) == 2*n && A048105(k+1) == 2*n;
a(n) = for(k=1, oo, if(isok(n, k), return(k))); \\ Daniel Suteu, May 16 2021

Crossrefs

Cf. A048105, A075036, A093548, A309181, A344314.

Sequence in context: A183427 A262852 A066414 * A042422 A180578 A301757

Adjacent sequences: A344312 A344313 A344314 * A344316 A344317 A344318

Keyword

nonn,more

Author

Amiram Eldar, May 14 2021

Extensions

a(13)-a(24) confirmed by Martin Ehrenstein, May 20 2021

Status

approved