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.

A347938 Primitive terms of A347935: terms of A347935 that are not multiples of other terms of A347935.

Original entry on oeis.org

60, 72, 108, 168, 252, 264, 280, 312, 396, 400, 468, 588, 612, 684, 816, 828, 880, 912, 924, 1040, 1044, 1092, 1104, 1116, 1232, 1332, 1360, 1392, 1428, 1456, 1476, 1520, 1548, 1568, 1596, 1692, 1716, 1840, 1890, 1908, 1932, 2124, 2196, 2200, 2244, 2288, 2320
Offset: 1

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Author

Amiram Eldar, Sep 20 2021

Keywords

Comments

Since any positive multiple of a term of A347935 is also a term of A347935, the sequence A347935 consists of the positive multiple of this sequence.

Examples

			The first 10 terms of A347935 are 60, 72, 108, 120, 144, 168, 180, 216, 240, 252. 120, 180 and 240 are multiples of 60, 144 is a multiple of 72, and 216 is a multiple of 108 and therefore they are not terms of this sequence. So, this sequence begins with 60, 72, 108, 168, 252.
		

Crossrefs

Subsequence of A005101 and A347935.

Programs

  • Mathematica
    abQ[n_] := DivisorSigma[1, n] > 2*n; s[n_] := DivisorSum[n, # &, abQ[#] &]; q[n_] := s[n] > 2*n && AllTrue[Most @ Divisors[n], ! q[#] &]; Select[Range[3000], q]

A347937 Numbers k such that k and k+1 are both terms of A347935.

Original entry on oeis.org

2282175, 16769024, 18356624, 27252224, 32493824, 35820224, 46577024, 50968575, 51962624, 53992575, 55130624, 61854975, 63101024, 63140175, 69980624, 72525375, 73378304, 74376224, 80791424, 82389824, 98834175, 102650624, 105674624, 107769375, 109001024, 110238975
Offset: 1

Views

Author

Amiram Eldar, Sep 20 2021

Keywords

Examples

			2282175 is a term since A187795(2282175) = 4801650 > 2*2282175 = 4564350 and A187795(2282176) = 4630080 > 2*2282176 = 4564352.
		

Crossrefs

Subsequence of A005101, A096399 and A347935.

Programs

  • Mathematica
    abQ[n_] := DivisorSigma[1, n] > 2*n; s[n_] := DivisorSum[n, # &, abQ[#] &]; q[n_] := s[n] > 2*n; seq = {}; q1 = q[1]; Do[q2 = q[n]; If[q1 && q2, AppendTo[seq, n-1]]; q1 = q2, {n, 2, 2*10^7}]; seq
  • PARI
    isok1(k) = sumdiv(k, d, if (sigma(d)>2*d, d)) > 2*k; \\ A347935
    isok(k) = isok1(k) && isok1(k+1); \\ Michel Marcus, Sep 20 2021

A347936 Odd numbers k such that A187795(k) > 2*k.

Original entry on oeis.org

155925, 225225, 259875, 294525, 297675, 363825, 405405, 429975, 467775, 496125, 552825, 562275, 571725, 606375, 628425, 675675, 694575, 760725, 765765, 779625, 883575, 893025, 921375, 945945, 987525, 1044225, 1091475, 1126125, 1167075, 1195425, 1216215, 1289925
Offset: 1

Views

Author

Amiram Eldar, Sep 20 2021

Keywords

Comments

The numbers of terms not exceeding 10^k for k = 6, 7, ... are 25, 352, 3281, 33291, 336686, ... Apparently, this sequence has an asymptotic density 0.000033...
Apparently, the least term that is not divisible by 3 is 836504377583875.

Examples

			The divisors of 155925 that are abundant numbers are {945, 1575, 2835, 3465, 4725, 5775, 7425, 10395, 14175, 17325, 22275, 31185, 51975, 155925}. Their sum is 330000 > 2*155925 = 311850. Therefore, 155925 is a term.
		

Crossrefs

The odd terms of A347935.
Subsequence of A005101 and A005231.
Cf. A187795.

Programs

  • Mathematica
    abQ[n_] := DivisorSigma[1, n] > 2*n; s[n_] := DivisorSum[n, # &, abQ[#] &]; q[n_] := s[n] > 2*n; Select[Range[1, 1000000, 2], q]
  • PARI
    isok(k) = (k%2) && sumdiv(k, d, if (sigma(d)>=2*d, d)) > 2*k; \\ Michel Marcus, Sep 20 2021
Showing 1-3 of 3 results.