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.

A281993 Integers m such that sigma(m) + sigma(2*m) = 6*m.

Original entry on oeis.org

10, 44, 184, 752, 12224, 49024, 12580864, 206158168064, 885443715520878608384, 226673591177468092350464, 232113757366000005450563584, 3894222643901120685369075227951104, 1020847100762815390371677078221595082752, 17126972312471518572699356075530215722269540352
Offset: 1

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Author

Michel Marcus, Feb 04 2017

Keywords

Comments

This is the case h = 2 of the h-perfect numbers as defined in the Harborth link.

Examples

			10 is a term since sigma(10) + sigma(20) = 60, that is 6*10.
		

Crossrefs

Programs

  • Mathematica
    Select[Range[10^7], DivisorSigma[1, #] + DivisorSigma[1, 2 #] == 6 # &] (* Michael De Vlieger, Feb 04 2017 *)
  • PARI
    isok(n, h=2) = sigma(n) + sigma(h*n) == 2*n*(h+1);

Formula

a(n) = 2^A002235(n+1) * A007505(n+1). - Daniel Suteu, Feb 08 2017 [See Harborth link for a proof.]

Extensions

More terms from Jinyuan Wang, Feb 11 2020

A097214 Numbers m such that A076078(m) = m, where A076078(m) equals the number of sets of distinct positive integers with a least common multiple of m.

Original entry on oeis.org

1, 2, 4, 8, 10, 16, 32, 44, 64, 128, 184, 256, 512, 752, 1024, 2048, 4096, 8192, 12224, 16384, 32768, 49024, 61064, 65536, 131072, 262144, 524288, 981520, 1048576, 2097152, 4194304, 8388608, 12580864, 16777216, 33554432, 67108864, 134217728
Offset: 1

Views

Author

Matthew Vandermast, Aug 12 2004

Keywords

Comments

Contains all powers of 2 (A000079). Union of A000079 and A097215.
If 3*2^k - 1 is prime then 2^k*(3*2^k-1) is in the sequence. So 2^A002235*(3*2^A002235-1) is a subsequence of this sequence. - Farideh Firoozbakht, Aug 06 2005

Examples

			A total of 10 sets of distinct positive integers have a least common multiple of 10: {1,2,5}, {1,2,5,10}, {1,2,10}, {1,5,10}, {1,10}, {2,5}, {2,5,10}, {2,10}, {5,10} and {10}. Hence 10 is in the sequence.
		

Crossrefs

Extensions

a(26) corrected by Jinyuan Wang, Feb 11 2020

A097416 Numbers n such that A076078(m)=n for some m, excluding powers of 2.

Original entry on oeis.org

10, 44, 184, 218, 400, 752, 3040, 3392, 3748, 12224, 27904, 49024, 57856, 61064, 64594, 196352, 226304, 253808, 785920, 954368, 981520, 1822720, 3144704, 12580864, 14630912, 15499264, 15722528, 16450240, 16700300, 31522816, 50327552
Offset: 1

Views

Author

Robert G. Wilson v, Aug 17 2004

Keywords

Comments

A076078(n) equals the number of sets of distinct positive integers with a least common multiple of n.

Crossrefs

Programs

  • Mathematica
    f[n_] := Block[{d = Divisors[n]}, Plus @@ (MoebiusMu[n/d](2^DivisorSigma[0, d] - 1))]; t = Union[ Table[ f[n], {n, 2^20}]]; Complement[ Take[t, 52], Table[2^i, {i, 0, 20}]]
Showing 1-3 of 3 results.