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.

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A265727 Least primitive weird number, pwn, (A002975) which is divisible by the n-th prime (A000040).

Original entry on oeis.org

70, 70, 836, 4030, 17272, 836, 7912, 7192, 4030, 113072, 83312, 7912, 8812312, 5830, 4199030, 9272, 91388, 10792, 23941578736, 786208, 682592, 569494624, 555616, 539744, 15126992, 73616, 519712
Offset: 3

Views

Author

Douglas E. Iannucci and Robert G. Wilson v, Dec 14 2015

Keywords

Comments

No odd weird number exists below 10^21. The search is done on the volunteer computing project yoyo@home. - Wenjie Fang, Feb 23 2014
As of Dec 14 2015, there is no known pwn which is divisible by 3. Therefore the offset denotes the third prime number, 5.

Examples

			a(6) is 4030 since it is the first pwn to be divisible by the sixth prime number, 13. 4030 = 13 * 310.
		

Crossrefs

Programs

  • Mathematica
    (* copy the terms from A002975, assign them equal to 'lst' and then *) f[n_] := Select[lst, Mod[#, Prime@ n] == 0 &][[1]]; Array[f, 27, 3]

A265726 Primitive weird numbers whose abundance is a record.

Original entry on oeis.org

70, 836, 7192, 9272, 73616, 243892, 338572, 1188256, 1901728, 3963968, 28279232, 36228736, 91322752, 141659096, 263144192, 351295232, 664373504, 2113834496, 5522263024, 6933503488, 19179527168, 22755515392, 31574500724, 98620009472, 135895635968
Offset: 1

Views

Author

Douglas E. Iannucci and Robert G. Wilson v, Dec 14 2015

Keywords

Comments

Although the abundance A(n) = sigma(n) - 2n is increasing, the (relative) abundancy sigma(n)/n is decreasing, except at indices {3, 6, 8, 15, 16, 19, 24 ...}. No term has larger abundancy than 2 + 2/35, that of a(1). - M. F. Hasler, Nov 14 2018

Examples

			a(1) = 70 since it is the first term in A002975; its abundance is 4.
a(2) is 836 since its abundance, 8, exceeds that of a(1); 4.
a(3) is 7192 = A002975(5) since its abundance, 16, exceeds that of a(2) and that of A002975(1..4).
		

Crossrefs

Programs

  • Mathematica
    (* copy the terms from A002975, assign them equal to 'lst' and then *) f[n_] := DivisorSigma[1, n] - 2n; k = 1; lsu = {}; mx = 0; While[k < 647, ds = f@ lst[[k]]; If[ds > mx, mx = ds; AppendTo[lsu, lst[[k]]]]; k++]; lsu
Showing 1-2 of 2 results.