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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A347384 Odd numbers k with such a unitary divisor d that A347381(d) > A347381(k).

Original entry on oeis.org

35, 105, 153, 189, 207, 279, 403, 423, 425, 437, 455, 475, 477, 575, 589, 639, 689, 725, 765, 775, 819, 833, 899, 923, 945, 963, 1025, 1035, 1071, 1127, 1143, 1175, 1209, 1271, 1275, 1311, 1325, 1341, 1365, 1391, 1395, 1421, 1425, 1449, 1475, 1495, 1519, 1651, 1719, 1725, 1739, 1767, 1775, 1791, 1881, 1927, 1953, 1961
Offset: 1

Views

Author

Antti Karttunen, Sep 10 2021

Keywords

Examples

			35 is a product of two primes, 5 and 7, with A347381(7) = 3 > A347381(35) = 2, therefore 35 is included in this sequence.

Links

Crossrefs

Cf. A347381.
Subsequences: A347390, A347383.

Programs

  • PARI
    isA347384(n) = if(!(n%2),0,my(w=A347381(n)); fordiv(n,d,if(1==gcd(d,n/d) && (A347381(d)>w), return(1))); (0));

A347888 Odd numbers k for which A003415(sigma(k^2))-(k^2) is strictly positive and a multiple of six. Here A003415 is the arithmetic derivative.

Original entry on oeis.org

273, 399, 651, 741, 903, 1209, 1407, 1533, 1659, 1677, 1767, 2037, 2163, 2331, 2451, 2457, 2613, 2667, 2847, 3003, 3081, 3297, 3423, 3591, 3685, 3783, 3819, 3843, 3885, 3999, 4017, 4095, 4161, 4179, 4329, 4345, 4389, 4431, 4503, 4683, 4953, 5061, 5187, 5529, 5691, 5817, 5859, 5871, 5985, 6123, 6231, 6279, 6327, 6357
Offset: 1

Views

Author

Antti Karttunen, Sep 19 2021

Keywords

Comments

A square root of any hypothetical odd term x (if such numbers exist) in A005820 (triperfect numbers) should be a member of this sequence. See comments in A347882, A347887 and also in A347870 and in A347391.
Of the first 200 terms of A097023, 44 appear also in this sequence, the first ones being 50281, 73535, 379953, etc.

Crossrefs

Intersection of A347882 and A347887. Subsequence of A347881 and of A347885.
Cf. A000203, A003415, A005820, A097023, A235991, A235992, A342923, A342925, A342926, A347383, A347391.

Programs

  • Mathematica
    ad[1] = 0; ad[n_] := n * Total@(Last[#]/First[#]& /@ FactorInteger[n]); Select[Range[1, 6500, 2], (d = ad[DivisorSigma[1, #^2]] - #^2) > 0 && Divisible[d, 6] &] (* Amiram Eldar, Sep 19 2021 *)
  • PARI
    A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
isA347888(n) = if(!(n%2),0,my(u=(A003415(sigma(n^2))-(n^2))); ((u>0)&&!(u%6)));
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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