A344315 - OEIS

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

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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