A190355 -id:A190355 - cp's OEIS frontend

A190646 Least number k such that d(k-1) = d(k+1) = 2n or 0 if no such k exists, where d(n)=A000005(n).

4, 7, 19, 41, 127252, 199, 26890624, 919, 17299, 6641, 25269208984376, 3401, 3900566650390624, 640063, 8418574, 18089, 1164385682220458984374, 41651, 69528379848480224609374, 128465, 34084859374, 12164095, 150509919493198394775390626, 90271

Offset: 1

Juri-Stepan Gerasimov, May 15 2011, May 20 2011

nonn

a(28) = 2319679. a(30) = 3568049.
From Chai Wah Wu, Mar 13 2019: (Start)
a(26) = 64505245697, a(27) = 3959299, a(29) = 237828698392557762563228607177734374, a(31) = 26711406049549496732652187347412109374, a(32) = 441559, a(34) = 12535291248641, a(36) = 352351, a(37) = 1749348542212388688829378224909305572509765626, a(38) = 193405731995647.
Conjecture: if p is an odd prime, then a(p) is even.
(End)

			a(16)=18089 because d(18088)=d(18090)=2*16.

Hugo van der Sanden, Table of n, a(n) for n = 1..40

Cf. A067888, A075036, A190355.

a(7), a(11), a(13), and a(15) from T. D. Noe, May 25 2011
a(17), a(19), a(21)-a(23) from Chai Wah Wu, Mar 13 2019
b-file extending to a(40) from Hugo van der Sanden, Mar 04 2022

A190645 Numbers n such that d(n-2) = d(n) = d(n+2) = 12 where d(n)=A000005(n).

Original entry on oeis.org

350, 738, 1276, 1314, 2890, 5052, 6356, 9052, 9054, 9950, 14050, 15966, 16852, 17916, 17948, 19166, 19852, 22475, 23348, 23420, 24350, 25182, 25184, 25186, 30476, 32418, 41058, 41060, 47646, 47648, 54927, 56452, 57436, 59924, 61794, 61796, 66787, 68348

Offset: 1

Juri-Stepan Gerasimov, May 15 2011

nonn

Numbers of the form A190355(n)+1 such that A190355(n)=A190355(n+1)-2.

G. C. Greubel, Table of n, a(n) for n = 1..5000

Cf. A000005(number of divisors of n), A190355.

f[n_] := DivisorSigma[0,n]; lst = {}; n = 2; While[Length[lst] < 40, n++; If[f[n-2] == f[n] == f[n+2] == 12, AppendTo[lst, n]]]; lst (* T. D. Noe, May 26 2011 *)
Select[Range[2, 5000], DivisorSigma[0, # - 2] == 12 && DivisorSigma[0, #] == 12 && DivisorSigma[0, # + 2] == 12 &] (* G. C. Greubel, Dec 29 2017 *)

isok(n) = (n>2) && (numdiv(n-2)==12) && (numdiv(n)==12) && (numdiv(n+2)==12); \\ Michel Marcus, Dec 30 2017

Corrected and extended by T. D. Noe, May 26 2011

cp's OEIS Frontend

A190646 Least number k such that d(k-1) = d(k+1) = 2n or 0 if no such k exists, where d(n)=A000005(n).

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