A085343 -id:A085343 - cp's OEIS frontend

A085122 a(n) = PrimePi(sigma(n)-phi(n)) - (PrimePi(sigma(n)) - PrimePi(phi(n))), where PrimePi = A000720, sigma = A000203 and phi = A000010.

0, -1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 1, 1, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 3, 3, 0, 2, 0, 3, 2, 2, 3, 3, 0, 3, 4, 3, 0, 4, 0, 3, 4, 3, 0, 4, 3, 5, 3, 5, 0, 3, 3, 3, 3, 3, 0, 3, 0, 4, 3, 4, 3, 4, 0, 5, 5, 5, 0, 4, 0, 2, 5, 4, 4, 4, 0, 5, 5, 5, 0, 7, 4, 5, 4, 5, 0, 4, 3, 5, 5, 5, 5, 4, 0, 5, 5, 5, 0, 6, 0, 6, 6, 7, 0, 5, 0, 5, 6, 8, 0, 5, 5, 6, 7, 5, 5, 5, 6, 5, 6, 7, 5, 5, 0, 7

Offset: 1

Labos Elemer, Jul 11 2003

Scatterplot of this sequence shows interesting strata. - Antti Karttunen, Jan 22 2020

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A000010, A000203, A000720, A051612, A070803, A070804, A085343.

t=Table[PrimePi[DivisorSigma[1, w]-EulerPhi[w]]- (PrimePi[DivisorSigma[1, w]]-PrimePi[EulerPhi[w]]), {w, 1, 10000}]

A085122(n) = (primepi(sigma(n)-eulerphi(n)) - (primepi(sigma(n))-primepi(eulerphi(n)))); \\ Antti Karttunen, Jan 22 2020

a(n) = A000720(A051612(n)) - (A070803(n) - A070804(n)) = A000720(A051612(n)) - A085343(n). - Antti Karttunen, Jan 22 2020

Name edited by Antti Karttunen, Jan 22 2020

A085346 Least number x so that number of primes between sigma(x) and phi(x) equals n.

Original entry on oeis.org

3, 2, 4, 6, 10, 14, 12, 26, 18, 34, 28, 32, 24, 62, 44, 30, 123, 40, 36, 64, 56, 106, 54, 48, 70, 66, 146, 105, 88, 78, 80, 135, 60, 178, 72, 102, 202, 112, 84, 164, 114, 90, 96, 154, 695, 231, 138, 108, 184, 1141, 176, 140, 126, 244, 132, 160, 326, 232, 186, 208, 120

Offset: 1

Labos Elemer, Jul 10 2003

nonn

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

Cf. A000720, A000010, A000203, A070803, A070804, A085341-A085347.

s(n) = my(f = factor(n)); primepi(sigma(f)) - primepi(eulerphi(f));
list(len) = {my(v = vector(len), k = 1, c = 0, i); while(c < len, i = s(k); if(i > 0 && i <= len && v[i] == 0, c++; v[i] = k); k++); v;} \\ Amiram Eldar, Dec 20 2024

a(n) = Min{x; A085343(x) = n}.

A085344 Least number x such that number of primes between sigma(x) and x equals n.

Original entry on oeis.org

2, 4, 10, 12, 16, 46, 28, 24, 44, 30, 42, 40, 36, 54, 48, 66, 178, 78, 104, 80, 102, 60, 128, 72, 84, 152, 90, 138, 255, 96, 108, 174, 140, 126, 132, 266, 160, 150, 248, 222, 156, 120, 246, 200, 144, 198, 634, 224, 220, 204, 370, 260, 168, 376, 555, 430, 354, 308

Offset: 1

Labos Elemer, Jul 10 2003

nonn

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

Cf. A000720, A000010, A000203, A070803, A070804.

Cf. A085341, A085342, A085343, A085345, A085346, A085347.

m = 100; seq = Table[0, {m}]; c = 0; n = 0; While[c < m, n++; i = PrimePi[ DivisorSigma[1, n]] - PrimePi[n]; If[i <= m && seq[[i]] == 0, c++; seq[[i]] = n]]; seq (* Amiram Eldar, Mar 01 2020 *)

a(n) = {my(x=1); while (primepi(sigma(x)) - primepi(x) != n, x++); x;} \\ Michel Marcus, Mar 01 2020

a(n) = Min{x; A085341(x)=n}.

cp's OEIS Frontend

A085122 a(n) = PrimePi(sigma(n)-phi(n)) - (PrimePi(sigma(n)) - PrimePi(phi(n))), where PrimePi = A000720, sigma = A000203 and phi = A000010.

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A085346 Least number x so that number of primes between sigma(x) and phi(x) equals n.

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PARI

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A085344 Least number x such that number of primes between sigma(x) and x equals n.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula