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.

A151797 Numbers which belong to just one of the two sequences A030229, A161918.

Original entry on oeis.org

1, 8, 210, 330, 390, 462, 510, 546, 570, 690, 714, 770, 798, 858, 870, 910, 930, 966, 1110, 1122, 1155, 1190, 1218, 1230, 1254, 1290, 1302, 1326, 1330, 1365, 1410, 1430, 1482, 1518, 1554, 1590, 1610, 1722, 1770, 1785, 1794, 1806, 1830, 1870, 1914, 1938, 1974
Offset: 1

Views

Author

M. F. Hasler, Jun 27 2009

Keywords

Crossrefs

Cf. A030229, A161918.

Programs

A161917 Numbers n for which the sum of their prime factors (with repetition) divides the sum of their divisors.

Original entry on oeis.org

12, 15, 35, 42, 60, 63, 66, 68, 84, 90, 95, 110, 114, 119, 140, 143, 152, 168, 189, 195, 204, 209, 216, 234, 245, 258, 264, 270, 280, 287, 290, 294, 297, 319, 322, 323, 352, 368, 377, 380, 384, 396, 470, 476, 480, 506, 510, 527, 531, 544, 552, 558, 559, 572
Offset: 1

Views

Author

Paolo P. Lava and Giorgio Balzarotti, Jun 23 2009

Keywords

Examples

			n=12: Sum_divisors (1,2,3,4,6,12) = 28; Sum_prime_factors (2,2,3) =7 -> 28/7 = 4. n=319: Sum_divisors (1,11,29,319) = 360; Sum_prime_factors (11,29) =40 -> 360/40 = 9.

Links

Crossrefs

Cf. A161918

Programs

  • Maple
    with(numtheory); P:=proc(q) local a,n;
for n from 2 to q do if not isprime(n) then a:=ifactors(n)[2];
if type(sigma(n)/add(a[k][1]*a[k][2],k=1..nops(a)),integer) then print(n);
fi; fi; od; end: P(10^4);
  • Mathematica
    Select[Range[2,600],Divisible[DivisorSigma[1,#],Total[ Times@@@ FactorInteger[#]]]&] (* Harvey P. Dale, Dec 09 2010 *)

Formula

{n: A001414(n) | A000203(n)}. - R. J. Mathar, Jun 26 2009

Extensions

Offset corrected by R. J. Mathar, Jun 26 2009

A328730 Dirichlet g.f.: Product_{k>=2} (1 - k^(-s))^k.

Original entry on oeis.org

1, -2, -3, -3, -5, 0, -7, 0, -6, 0, -11, 9, -13, 0, 0, 2, -17, 12, -19, 15, 0, 0, -23, 18, -15, 0, -1, 21, -29, 30, -31, 12, 0, 0, 0, 33, -37, 0, 0, 30, -41, 42, -43, 33, 30, 0, -47, 30, -28, 30, 0, 39, -53, 38, 0, 42, 0, 0, -59, 60, -61, 0, 42, 14, 0, 66, -67, 51, 0, 70
Offset: 1

Views

Author

Ilya Gutkovskiy, Oct 26 2019

Keywords

Comments

Dirichlet inverse of A050367.

Crossrefs

Cf. A050367, A114592, A161918 (positions of 0's), A328731.

Formula

a(1) = 1; a(n) = -Sum_{d|n, dA050367(n/d) * a(d).
Showing 1-3 of 3 results.

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

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