A067889 -id:A067889 - cp's OEIS frontend

A145340 a(n) = the maximum of d(p(n)-1) and d(p(n)+1), where d(m) is the number of divisors of m and p(n) is the n-th prime.

2, 3, 4, 4, 6, 6, 6, 6, 8, 8, 8, 9, 8, 8, 10, 8, 12, 12, 8, 12, 12, 10, 12, 12, 12, 9, 8, 12, 12, 10, 12, 12, 8, 12, 12, 12, 12, 10, 16, 8, 18, 18, 14, 14, 12, 12, 16, 12, 12, 12, 12, 20, 20, 18, 9, 16, 16, 16, 12, 16, 8, 12, 12, 16, 16, 8, 16, 20, 12, 12, 12, 24, 10, 12, 16, 16, 16

Offset: 1

Leroy Quet, Oct 08 2008

nonn

Cf. A145339, A008328, A008329, A067889, A103664, A103665.

Table[Max[DivisorSigma[0, Prime[n]-1], DivisorSigma[0, Prime[n]+1]], {n, 1, 100}] (* Stefan Steinerberger, Oct 11 2008 *)

More terms from Stefan Steinerberger and Ray Chandler, Oct 11 2008

A171669 Pell numbers sandwiched between two numbers having same number of divisors.

Original entry on oeis.org

12, 5741, 2744210, 15994428, 21300003689580, 723573111879672, 1111984844349868137938112, 293199986221627877463941823267862, 9960168529794442859224531878561050, 27749033099085295754434173207717704165, 66992092050551637663438906713182313772

Offset: 1

Vladimir Joseph Stephan Orlovsky, Dec 14 2009

nonn

Amiram Eldar, Table of n, a(n) for n = 1..19

Cf. A000005, A000129, A005237, A005238, A067889, A171666, A171667, A171668.

f[n_]:=Length[Divisors[n]]; a=1;b=0;c=0;lst={};Do[c=a+b+c;If[f[c-1]==f[c+1],AppendTo[lst,c]];a=b;b=c,{n,80}];lst

a(8)-a(11) from Amiram Eldar, Aug 08 2024

A192220 Semiprimes s such that tau(s-1) = tau(s+1) where tau = A000005.

Original entry on oeis.org

4, 6, 9, 34, 51, 55, 86, 94, 129, 142, 183, 185, 202, 214, 218, 247, 249, 302, 341, 394, 415, 446, 471, 473, 535, 583, 634, 698, 723, 737, 807, 851, 905, 922, 926, 949, 1042, 1138, 1149, 1205, 1211, 1241, 1257, 1262, 1313, 1315, 1337, 1346, 1402, 1527, 1546, 1577, 1594, 1642, 1646, 1673, 1687

Offset: 1

Juri-Stepan Gerasimov, Jun 26 2011

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000005, A001358, A067888, A067889.

Select[Range[2000], PrimeOmega[#] == 2 && Equal @@ DivisorSigma[0, # + {-1, 1}] &] (* Amiram Eldar, Jan 23 2025 *)

isok(k) = bigomega(k) == 2 && numdiv(k-1) == numdiv(k+1); \\ Amiram Eldar, Jan 23 2025

A001358 INTERSECT A067888.

A356766 Least number k such that k and k+2 both have exactly 2n divisors, or -1 if no such number exists.

Original entry on oeis.org

3, 6, 18, 40, 127251, 198, 26890623, 918, 17298, 6640, 25269208984375, 3400, 3900566650390623, 640062, 8418573, 18088, 1164385682220458984373, 41650, 69528379848480224609373, 128464, 34084859373, 12164094, 150509919493198394775390625, 90270, 418514293125, 64505245696

Offset: 1

Jean-Marc Rebert, Aug 26 2022

nonn

			For n=1, numdiv(3) = numdiv(5) = 2 = 2*1, and no number < 3 satisfies this, hence a(1) = 3.

Numbers k such that k and k+2 both have exactly m divisors: A001359 (m=2), A356742 (m=4), A356743 (m=6), A356744 (m=8).

Cf. A000005 (d(n)), A003680, A005238, A006558, A006601, A062832, A067888, A067889, A075036.

a={}; n=1; nmax=10; For[k=1, n<=nmax, k++, If[DivisorSigma[0, k] == DivisorSigma[0, k+2] == 2n, AppendTo[a, k]; k=1; n++]]; a (* Stefano Spezia, Aug 26 2022 *)
Flatten[Table[SequencePosition[DivisorSigma[0,Range[27*10^6]],{2n,,2n},1],{n,10}],1][[;;,1]] (* The program generates the first 10 terms of the sequence. To generate more, increase the Range constant but the program will take a long time to run. *) (* _Harvey P. Dale, Jul 01 2023 *)

a(n)=for(k=1,+oo,if(numdiv(k)==2*n&&numdiv(k+2)==2*n,return(k)))

More terms from Jinyuan Wang, Aug 28 2022

cp's OEIS Frontend

A145340 a(n) = the maximum of d(p(n)-1) and d(p(n)+1), where d(m) is the number of divisors of m and p(n) is the n-th prime.

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A171669 Pell numbers sandwiched between two numbers having same number of divisors.

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A192220 Semiprimes s such that tau(s-1) = tau(s+1) where tau = A000005.

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A356766 Least number k such that k and k+2 both have exactly 2n divisors, or -1 if no such number exists.

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