A175143 -id:A175143 - cp's OEIS frontend

A092405 a(n) = tau(n) + tau(n+1), where tau(n) = A000005(n), the number of divisors of n.

3, 4, 5, 5, 6, 6, 6, 7, 7, 6, 8, 8, 6, 8, 9, 7, 8, 8, 8, 10, 8, 6, 10, 11, 7, 8, 10, 8, 10, 10, 8, 10, 8, 8, 13, 11, 6, 8, 12, 10, 10, 10, 8, 12, 10, 6, 12, 13, 9, 10, 10, 8, 10, 12, 12, 12, 8, 6, 14, 14, 6, 10, 13, 11, 12, 10, 8, 10, 12, 10, 14, 14, 6, 10, 12, 10, 12, 10, 12, 15, 9, 6, 14, 16

Offset: 1

Jon Perry, Mar 22 2004

nonn

If a child is born to an n-year-old parent, this is the number of times the age of the parent will be a multiple of the age of the child. E.g., if n = 27, this will happen at the ages (28, 1), (29, 1),(30, 2), (30, 3), (32, 4), (35, 7), (42, 14), (36, 9), (54, 27), (56, 28). - Alexander Piperski, Sep 10 2018

Antti Karttunen, Table of n, a(n) for n = 1..20000

Cf. A000005, A092403, A175143, A346562.

Total /@ Partition[Array[DivisorSigma[0, #] &, 85], 2, 1] (* Michael De Vlieger, Sep 18 2018 *)

for(i=1,60,print1(","sigma(i,0)+sigma(i+1,0)))

A092405(n) = (numdiv(n)+numdiv(1+n)); \\ Antti Karttunen, Oct 07 2017

a(n) = A346562(n+1,n). - Omar E. Pol, Jul 23 2021

Extended by Ray Chandler, Mar 05 2010

A333053 Numbers m such that min(d(m), d(m+1)) > min(d(k), d(k+1)) for all k < m, where d(m) is the number of divisors of m (A000005).

Original entry on oeis.org

1, 2, 8, 14, 44, 104, 224, 495, 735, 2024, 2079, 5264, 5984, 21735, 126224, 201824, 862784, 1890944, 2821455, 6116175, 7316000, 14753024, 23014719, 38127375, 80061344, 205466624, 391738599, 879207615, 1794220064, 3199900599, 3809727999, 16916370624

Offset: 1

Amiram Eldar, Mar 06 2020

The corresponding values of min(d(a(n)), d(a(n)+1)) are 1, 2, 3, 4, 6, 8, 9, 10, 12, 15, 16, 20, 24, 32, 40, 48, 56, 64, 72, 80, 96, 108, 112, 120, 144, 160, 192, 224, 240, 256, 288, 320, ...

			The values of min(d(k), d(k+1)) for k = 1, 2, ... 8 are 1, 2, 2, 2, 2, 2, 2, 3. The record values in this range, 1, 2 and 3, are obtained at k = 1, 2, and 8.

Cf. A000005, A002182, A123000, A175143, A333054.

seq={}; dminmax = 0; d1 = 1; Do[d2 = DivisorSigma[0, n];dmin = Min[d1, d2]; If[dmin > dminmax, dminmax = dmin; AppendTo[seq, n-1]]; d1 = d2, {n, 2, 10^6}]; seq

A333052 Numbers m such that d(m) = d(m+1) and d(k) < d(m) for all k < m such that d(k) = d(k+1), where d(m) is the number of divisors of m (A000005).

Original entry on oeis.org

2, 14, 44, 104, 735, 2295, 5264, 5984, 21735, 201824, 3341624, 6481475, 7316000, 49727600, 103488384, 205684479, 349167104, 391738599, 1921172175, 6110171144, 7616307699

Offset: 1

Amiram Eldar, Mar 06 2020

The corresponding numbers of divisors are 2, 4, 6, 8, 12, 16, 20, 24, 32, 48, 64, 72, 96, 120, 128, 144, 160, 192, 240, 256, 288, ...

			2 is a term since (2, 3) is the first pair of consecutive numbers with the same number of divisors: d(2) = d(3) = 2.
14 is a term since d(14) = d(15) = 4 > d(2) = 2.
44 is a term since d(44) = d(45) = 6 > d(14) = 4.

Cf. A000005, A002182, A005237, A175143.

seq = {}; dmax = 0; d1 = 1; Do[If[d1 == (d2 = DivisorSigma[0, n]) && d1 > dmax, dmax = d1; AppendTo[seq, n-1]]; d1 = d2, {n, 2, 10^4}]; seq

cp's OEIS Frontend

A092405 a(n) = tau(n) + tau(n+1), where tau(n) = A000005(n), the number of divisors of n.

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A333053 Numbers m such that min(d(m), d(m+1)) > min(d(k), d(k+1)) for all k < m, where d(m) is the number of divisors of m (A000005).

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A333052 Numbers m such that d(m) = d(m+1) and d(k) < d(m) for all k < m such that d(k) = d(k+1), where d(m) is the number of divisors of m (A000005).

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