A161912 -id:A161912 - cp's OEIS frontend

A162197 a(n) = A161912(n) - A061358(n).

0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 6, 3, 3, 2, 5, 5, 7, 5, 8, 3, 6, 4, 11, 8, 11, 7, 10, 4, 8, 11, 15, 14, 13, 16, 18, 11, 19, 17, 20, 16, 19, 17, 20, 16, 14, 19, 33, 22, 25, 20, 26, 19, 30, 23, 29, 25, 26, 24, 30, 14, 27, 35, 35, 26

Offset: 0

Omar E. Pol, Jul 04 2009

Cf. A006218, A040976, A061358, A161911, A161912, A161913.

a(n) = A040976(n+1) - A006218(n) - A061358(n).

A162339 Numbers A161912 such that a(n)<>a(n+1).

Original entry on oeis.org

0, 1, 4, 2, 6, 4, 6, 7, 9, 5, 7, 11, 12, 10, 6, 8, 14, 16, 14, 20, 18, 15, 19, 21, 19, 21, 19, 15, 23, 33, 27, 26, 24, 26, 22, 30, 28, 30, 28, 26, 28, 30, 20, 28, 38, 36, 31, 37, 41, 45, 43, 39, 43, 39, 43, 45, 43, 47, 43, 49, 46, 52

Offset: 1

Omar E. Pol, Jul 04 2009

nonn

Cf. A161911, A161912, A161913, A162188, A162189.

A161911 a(n) is the n-th difference between consecutive primes minus the number of divisors of n.

Original entry on oeis.org

0, 0, 0, 1, 0, 0, 0, 0, 3, -2, 4, -2, 0, 0, 2, 1, 0, 0, 2, -4, 2, 0, 4, 0, 1, -2, 0, -4, 2, 6, 2, 0, -2, 6, -2, -3, 4, 0, 2, -2, 0, 2, 0, -2, -4, 8, 10, -6, -1, -2, 2, -4, 8, -2, 2, -2, -2, 2, 2, -10, 8, 10, -2, -5, 0, 6, 4, 4, -2, -4, 4, -4, 4, 2, -2, 0, 4, -4, 6, 0, -3, 6, 0, -6, 0, 2, 4, -4

Offset: 1

Omar E. Pol, Jun 28 2009

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Omar E. Pol, Illustration: Divisors and pi(x)

Cf. A000005, A001223, A161912.

A001223 := proc(n) ithprime(n+1)-ithprime(n) ; end: A000005 := proc(n) numtheory[tau](n) ; end: A161911 := proc(n) A001223(n)-A000005(n) ; end: seq(A161911(n),n=1..120) ; # R. J. Mathar, Jul 01 2009

With[{nn=90},#[[1]]-DivisorSigma[0,#[[2]]]&/@Thread[{Differences[Prime[ Range[ nn]]],Range[nn-1]}]] (* Harvey P. Dale, Oct 01 2018 *)

a(n) = A001223(n) - A000005(n).

More terms from R. J. Mathar, Jul 01 2009

A161913 Numbers k such that A001223(k) <> A000005(k).

Original entry on oeis.org

4, 9, 10, 11, 12, 15, 16, 19, 20, 21, 23, 25, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 39, 40, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 77, 78

Offset: 1

Omar E. Pol, Jul 04 2009

Nathaniel Johnston, Table of n, a(n) for n = 1..10000
Omar E. Pol, Illustration: Divisors and pi(x)

Cf. A000005, A001223, A068526, A161911, A161912, A162188, A162189.

p2:=2:for n from 1 to 78 do p1:=p2:p2:=ithprime(n+1):if(p2-p1<>tau(n))then print(n);fi:od: # Nathaniel Johnston, Apr 15 2011

A162188 Numbers k such that A001223(k) > A000005(k).

Original entry on oeis.org

4, 9, 11, 15, 16, 19, 21, 23, 25, 29, 30, 31, 34, 37, 39, 42, 46, 47, 51, 53, 55, 58, 59, 61, 62, 66, 67, 68, 71, 73, 74, 77, 79, 82, 86, 87, 91, 92, 94, 97, 99, 101, 103, 106, 107, 111, 114, 115, 118, 119, 121, 123, 124, 125, 127, 129, 131, 133, 137, 138, 139, 141, 145

Offset: 1

Omar E. Pol, Jul 04 2009

Franklin T. Adams-Watters, Table of n, a(n) for n = 1..5000
Omar E. Pol, Illustration: Divisors and pi(x)

Cf. A000005, A001223, A068526, A161911, A161912, A161913, A162189.

for(n=1,200,if(prime(n+1)-prime(n)>numdiv(n),print1(n","))) \\ Franklin T. Adams-Watters, May 26 2010

More terms from Franklin T. Adams-Watters, May 26 2010

A162189 Numbers k such that A001223(k) < A000005(k).

Original entry on oeis.org

10, 12, 20, 26, 28, 33, 35, 36, 40, 44, 45, 48, 49, 50, 52, 54, 56, 57, 60, 63, 64, 69, 70, 72, 75, 78, 81, 84, 88, 90, 96, 98, 100, 102, 104, 105, 108, 110, 112, 116, 117, 120, 126, 130, 132, 136, 140, 142, 144, 147, 148, 152, 153, 156, 160, 165

Offset: 1

Omar E. Pol, Jul 04 2009

Nathaniel Johnston, Table of n, a(n) for n = 1..10000
Omar E. Pol, Illustration: Divisors and pi(x)

Cf. A000005, A001223, A068526, A161911, A161912, A161913, A162188.

p2:=2:for n from 1 to 200 do p1:=p2:p2:=ithprime(n+1):if(p2-p1Nathaniel Johnston, Apr 15 2011

a(30)-a(56) from Nathaniel Johnston, Apr 15 2011

cp's OEIS Frontend

A162197 a(n) = A161912(n) - A061358(n).

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A162339 Numbers A161912 such that a(n)<>a(n+1).

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A161911 a(n) is the n-th difference between consecutive primes minus the number of divisors of n.

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Formula

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A161913 Numbers k such that A001223(k) <> A000005(k).

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Maple

A162188 Numbers k such that A001223(k) > A000005(k).

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PARI

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A162189 Numbers k such that A001223(k) < A000005(k).

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Programs

Maple

Extensions