cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A090340 Difference between the sums of the prime factors, including multiplicity, of n and those of n + 1.

Original entry on oeis.org

-2, -1, -1, -1, 0, -2, 1, 0, -1, -4, 4, -6, 4, 1, 0, -9, 9, -11, 10, -1, -3, -10, 14, -1, -5, 6, -2, -18, 19, -21, 21, -4, -5, 7, 2, -27, 16, 5, 5, -30, 29, -31, 28, 4, -14, -22, 36, -3, 2, -8, 3, -36, 42, -5, 3, -9, -9, -28, 47, -49, 28, 20, 1, -6, 2, -51, 46, -5, 12, -57, 59, -61, 34, 26, -10, 5, 0, -61, 66, 1, -31, -40, 69, -8, -23, 13
Offset: 1

Views

Author

Charles K. Layman (cklayman(AT)juno.com), Nov 25 2003

Keywords

Comments

If a(n) = 0 then n is a Ruth-Aaron number. - Andrew Slattery, Apr 15 2020

Examples

			a(24)=-1 because 24=2*2*2*3, 25=5*5 and (2+2+2+3)-(5+5)=-1.

Crossrefs

Cf. A001414 (sopfr), A090341, A090342, A090343.
Ruth-Aaron numbers: A039752.

Formula

a(n) = sopfr(n) - sopfr(n+1), where sopfr = A001414. - Wesley Ivan Hurt, Aug 10 2016

A090341 Difference between the sums of the prime factors, including multiplicity, of n and those of n + 2.

Original entry on oeis.org

-3, -2, -2, -1, -2, -1, 1, -1, -5, 0, -2, -2, 5, 1, -9, 0, -2, -1, 9, -4, -13, 4, 13, -6, 1, 4, -20, 1, -2, 0, 17, -9, 2, 9, -25, -11, 21, 10, -25, -1, -2, -3, 32, -10, -36, 14, 33, -1, -6, -5, -33, 6, 37, -2, -6, -18, -37, 19, -2, -21, 48, 21, -5, -4, -49, -5, 41, 7, -45, 2, -2, -27, 60, 16, -5, 5, -61, 5, 67, -30, -71, 29, 61, -31, -10
Offset: 1

Views

Author

Charles K. Layman (cklayman(AT)juno.com), Nov 25 2003

Keywords

Examples

			a(24)=-6 because 24=2*2*2*3, 26=2*13 and (2+2+2+3)-(2+13)=-6.

Crossrefs

Cf. A001414, A090340, A090342, A090343.

Programs

  • Mathematica
    Join[{-3},#[[1]]-#[[3]]&/@Partition[Table[Total[Flatten[Table[#[[1]], #[[2]]]& /@ FactorInteger[n]]],{n,2,90}],3,1]] (* Harvey P. Dale, Apr 06 2018 *)

Formula

a(n) = A001414(n) - A001414(n+2). - Wesley Ivan Hurt, Aug 29 2016

A090343 Difference between the sums of the prime factors, including multiplicity, of n and those of n + 4.

Original entry on oeis.org

-5, -3, -4, -2, -1, -2, -4, -1, -7, -2, 3, -1, -4, 1, -11, -1, 7, -5, -4, 0, 0, -2, 14, -2, -19, 5, -22, 1, 15, -9, 19, 0, -23, -2, -4, -1, -4, 9, -27, -4, 30, -13, -4, 4, -3, 13, 27, -6, -39, 1, 4, 4, 31, -20, -43, 1, -39, -2, 46, 0, 43, 17, -54, -9, -8, 2, -4, 9, -47, -25, 58, -11, 55, 21, -66, 10, 6, -25, -4, -1, -10, -2, 51, -3, -67
Offset: 1

Views

Author

Charles K. Layman (cklayman(AT)juno.com), Nov 25 2003

Keywords

Examples

			a(24)=-2 because 24=2*2*2*3, 28=2*2*7 and (2+2+2+3)-(2+2+7)=-2.

Crossrefs

Cf. A001414, A090340, A090341, A090342.

Programs

  • Mathematica
    Join[{-5},#[[1]]-#[[5]]&/@Partition[Table[Total[Times@@@FactorInteger[n]],{n,2,90}],5,1]] (* Harvey P. Dale, Jul 02 2022 *)

Formula

a(n) = A001414(n) - A001414(n+4). - Wesley Ivan Hurt, Aug 29 2016
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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