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.

Previous Showing 71-80 of 1775 results. Next

A116025 sigma(n) plus n gives a semiprime (A001358).

Original entry on oeis.org

7, 9, 14, 15, 17, 18, 19, 20, 22, 32, 39, 43, 45, 46, 47, 49, 50, 51, 59, 61, 62, 68, 70, 71, 72, 79, 81, 86, 91, 93, 95, 101, 104, 107, 109, 110, 115, 116, 117, 118, 121, 123, 129, 130, 142, 149, 151, 158, 160, 163, 164, 165, 167, 177, 185, 187, 197, 201, 207
Offset: 1

Views

Author

Giovanni Resta, Feb 13 2006

Keywords

Examples

			sigma(101)+101=203=7*29.

Links

Crossrefs

Cf. A001358, A116014.

Programs

  • Mathematica
    Select[Range[300],PrimeOmega[DivisorSigma[1,#]+#]==2&] (* Harvey P. Dale, May 21 2014 *)

A116046 n+phi(n)+phi(phi(n)) is a semiprime (A001358).

Original entry on oeis.org

2, 3, 6, 7, 8, 11, 14, 18, 23, 27, 29, 31, 34, 37, 38, 42, 45, 47, 53, 55, 59, 63, 65, 66, 69, 73, 74, 83, 89, 90, 91, 93, 103, 105, 107, 109, 110, 117, 119, 123, 125, 127, 129, 130, 131, 138, 139, 143, 145, 150, 151, 157, 167, 174, 175, 179, 182, 183, 185, 186
Offset: 1

Views

Author

Giovanni Resta, Feb 13 2006

Keywords

Examples

			103+phi(103)+phi(phi(103)) = 3*79.

Crossrefs

Cf. A001358, A116045.

A116051 n+sigma(n)+sigma(sigma(n)) is a semiprime (A001358).

Original entry on oeis.org

2, 3, 6, 11, 13, 17, 20, 33, 39, 45, 47, 52, 57, 58, 59, 61, 63, 64, 69, 81, 83, 85, 86, 89, 91, 98, 100, 103, 110, 115, 117, 123, 128, 133, 134, 135, 136, 141, 142, 143, 144, 145, 149, 150, 153, 154, 156, 158, 162, 164, 167, 173, 179, 181, 184, 185, 187, 189
Offset: 1

Views

Author

Giovanni Resta, Feb 13 2006

Keywords

Examples

			115 + sigma(115) + sigma(sigma(115)) = 662 = 2*331

Crossrefs

Cf. A001358.

A116063 Semiprimes (A001358) made of nontrivial runs of identical digits.

Original entry on oeis.org

22, 33, 55, 77, 111, 1111, 1133, 1177, 1199, 3377, 4411, 4499, 5533, 5599, 6611, 6677, 7711, 7799, 8899, 9977, 11111, 11199, 11333, 11555, 22233, 22255, 22299, 22333, 22999, 33322, 44222, 44333, 44411, 44477, 44999, 55111, 55222, 55577
Offset: 1

Views

Author

Giovanni Resta, Feb 13 2006

Keywords

Comments

A run of length 1 is trivial.

Examples

			44477 = 79*563

Crossrefs

Cf. A001358, A033023, A116062.

A133980 Home primes of semiprimes (A001358).

Original entry on oeis.org

23, 37, 211, 223, 229, 241, 271, 283, 311, 313, 317, 331, 337, 347, 353, 359, 367, 373, 379, 383, 389, 397, 523, 541, 547, 571, 719, 743, 761, 773, 797, 1117, 1123, 1129, 1153, 1171, 1319, 1361, 1367, 1373, 1723, 1741, 1747, 1753, 1759, 1783, 1789, 1931
Offset: 1

Views

Author

Jonathan Vos Post & Robert G. Wilson v, Oct 01 2007, Oct 06 2007

Keywords

Comments

Not the same as A133957.
Number of terms < 10^n: 0, 2, 31, 223, 1638, 11752, 89918, ....

Crossrefs

Cf. A001358, A133955, A133957.

Programs

  • Mathematica
    lst = {}; semiPrimeQ[x_] := Plus @@ Last /@ FactorInteger@x == 2; f[n_] := FromDigits@ Flatten[IntegerDigits@ Table[ #[[1]], {#[[2]]}] & /@ FactorInteger@n, 2]; h[n_] := NestWhileList[ f@# &, n, ! PrimeQ@# &, 1, 6];

A142862 Semiprimes n (A001358) for which A000001(n) is 1.

Original entry on oeis.org

15, 33, 35, 51, 65, 69, 77, 85, 87, 91, 95, 115, 119, 123, 133, 141, 143, 145, 159, 161, 177, 185, 187, 209, 213, 215, 217, 221, 235, 247, 249, 259, 265, 267, 287, 295, 299, 303, 319, 321, 323, 329, 335, 339, 341, 365, 371, 377, 391, 393, 395, 403, 407, 411
Offset: 1

Views

Author

N. J. A. Sloane, Oct 03 2008

Keywords

Comments

Semiprimes pq with pT. D. Noe, Oct 08 2008

References

  • D. S. Dummit and R. M. Foote, Abstract Algebra, Wiley, 3rd Edition, 2003, page 135.

Links

Crossrefs

Cf. A050384, A003277. [Franklin T. Adams-Watters, Feb 27 2009]

Programs

  • Mathematica
    Select[Select[Range[1000],FactorInteger[#][[All, 2]] == {1, 1} &], !
Divisible[FactorInteger[#][[2, 1]] - 1, FactorInteger[#][[1, 1]]] &] (* Geoffrey Critzer, Nov 07 2015 *)

Extensions

More terms from R. J. Mathar, Oct 04 2008

A142863 Semiprimes n (A001358) for which A000001(n) is 2.

Original entry on oeis.org

4, 6, 9, 10, 14, 21, 22, 25, 26, 34, 38, 39, 46, 49, 55, 57, 58, 62, 74, 82, 86, 93, 94, 106, 111, 118, 121, 122, 129, 134, 142, 146, 155, 158, 166, 169, 178, 183, 194, 201, 202, 203, 205, 206, 214, 218, 219, 226, 237, 253, 254, 262, 274, 278, 289, 291, 298, 301
Offset: 1

Views

Author

N. J. A. Sloane, Oct 03 2008

Keywords

Comments

Semiprimes p^2 or pq with pT. D. Noe, Oct 08 2008

Links

Crossrefs

Cf. A000001, A001358.

Extensions

More terms from R. J. Mathar, Oct 04 2008

A146482 Decimal expansion of Product_{q in A001358} (1-1/(q*(q-1))).

Original entry on oeis.org

8, 3, 9, 0, 4, 2, 1, 5, 4, 2, 7, 4, 4, 6, 8, 6, 0, 0, 7, 6, 8, 4, 6, 2, 1, 1, 1, 1, 9, 4, 5, 4, 1, 2, 5, 4, 9, 2, 8, 3, 0, 7, 1, 6, 6, 7, 6, 0, 8, 8, 2, 7, 3, 3, 0, 0, 0
Offset: 0

Views

Author

R. J. Mathar, Feb 13 2009

Keywords

Comments

Semiprime analog of A005596.

Examples

			0.839042154274468600768... = (1-1/12)*(1-1/30)*(1-1/72)*(1-1/90)*(1-1/182)*..

Links

Formula

The logarithm is -sum_{s>=2} sum_{j=1..floor[s/(1+r)]} binomial(s-r*j-1,j-1)*P_2(s)/j at r=1, where P_k(s) are the k-almost prime zeta functions of arXiv:0803.0900.

A146486 Decimal expansion of Product_{q in A001358} (1-1/(q^2*(q-1))).

Original entry on oeis.org

9, 6, 9, 9, 3, 2, 3, 2, 5, 0, 0, 1, 5, 2, 5, 3, 1, 6, 2, 1, 4, 9, 2, 0, 2, 0, 7, 7, 8, 9, 1, 2, 9, 5, 7, 5, 9, 6, 1, 1, 4, 5, 7, 9, 4, 7, 9, 6, 6, 9, 6, 0, 8, 8, 0, 0, 6
Offset: 0

Views

Author

R. J. Mathar, Feb 13 2009

Keywords

Comments

Semiprime analog of A065414.

Examples

			0.969932325001525316214920... = (1-1/48)*(1-1/180)*(1-1/648)*(1-1/900)*..

Links

A154928 Decimal expansion of Sum_{q in A001358} log(q)/q^2 over the semiprimes q = 4,6,9,...

Original entry on oeis.org

0, 2, 8, 3, 6, 0, 6, 8, 1, 5, 4, 0, 7, 9, 8, 0, 6, 5, 2, 2, 2, 4, 2, 5, 8, 2, 2, 2, 5, 4, 8, 2, 7, 8, 3, 3, 6, 0, 7, 9, 3, 5, 0, 5, 7, 8, 2, 3, 7, 8, 1, 4, 0, 1, 3, 4, 1, 1, 1, 1
Offset: 0

Views

Author

R. J. Mathar, Jan 17 2009

Keywords

Comments

Semiprime analog of A136271. The absolute value of the first derivative of the semiprime zeta function at 2.

Examples

			Equals 0.0283606815... = log(4)/16 + log(6)/36 + log(9)/81 + ....

Links

Formula

Equals Sum_{j>=1} log(A001358(j))/A074985(j).

Extensions

Missing zero inserted. Artur Jasinski, Jul 29 2025
Previous Showing 71-80 of 1775 results. Next

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

Content is available under The OEIS End-User License Agreement.