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 1-4 of 4 results.

A108607 4-almost primes whose sum of factors is a prime.

Original entry on oeis.org

40, 54, 56, 88, 90, 104, 136, 184, 198, 210, 248, 250, 294, 296, 328, 350, 376, 390, 414, 424, 462, 488, 522, 536, 550, 570, 584, 664, 686, 714, 776, 798, 808, 824, 850, 856, 858, 930, 950, 954, 1014, 1048, 1062, 1110, 1190, 1208, 1210, 1218, 1256, 1274, 1278
Offset: 1

Views

Author

Zak Seidov, Jun 12 2005

Keywords

Examples

			40=2*2*2*5 (4-almost prime) and 2+2+2+5=11 is a prime.

Links

Crossrefs

Cf. A107707, A108608, A108609 (resp.) 3, 5, 6 (resp.)-almost primes whose sum of factors is a prime.

Programs

  • PARI
    is(n)=my(f=factor(n));sum(i=1,#f~,f[i,2])==4 && isprime(sum(i=1,#f~,f[i,1]*f[i,2])) \\ Charles R Greathouse IV, Oct 11 2013

A108608 5-almost primes whose sum of factors is a prime.

Original entry on oeis.org

48, 80, 108, 176, 252, 300, 368, 405, 420, 464, 468, 500, 567, 660, 675, 684, 848, 891, 944, 980, 1020, 1116, 1136, 1140, 1323, 1332, 1377, 1424, 1428, 1452, 1539, 1548, 1575, 1616, 1700, 1716, 1740, 1820, 1860, 1875, 1932, 2096, 2156, 2196, 2295, 2300
Offset: 1

Views

Author

Zak Seidov, Jun 12 2005

Keywords

Examples

			48=2*2*2*2*3 (5-almost prime) and 2+2+2+2+3=11 is a prime.

Links

Crossrefs

Cf. A107707, A108607, A108609 (resp.) 3, 4, 6 (resp.)-almost primes whose sum of factors is a prime.

Programs

  • Mathematica
    Select[Range[2500],PrimeOmega[#]==5&&PrimeQ[Total[Times@@@FactorInteger[#]]]&] (* Harvey P. Dale, Apr 07 2022 *)
  • PARI
    is(n)=my(f=factor(n));sum(i=1,#f~,f[i,2])==5 && isprime(sum(i=1,#f~,f[i,1]*f[i,2])) \\ Charles R Greathouse IV, Oct 11 2013

A108609 6-almost primes whose sum of factors is a prime.

Original entry on oeis.org

96, 224, 360, 416, 486, 504, 600, 608, 792, 810, 992, 1176, 1184, 1224, 1368, 1376, 1400, 1890, 1952, 2040, 2088, 2184, 2232, 2250, 2336, 2528, 2600, 2754, 2760, 2904, 2952, 3080, 3104, 3296, 3384, 3480, 3510, 3640, 3726, 4064, 4158, 4248, 4312, 4392
Offset: 1

Views

Author

Zak Seidov, Jun 12 2005

Keywords

Examples

			96=2*2*2*2*2*3 (6-almost prime) and 2+2+2+2+2+3=13 is a prime.

Links

Crossrefs

Cf. A107707, A108607, A108608 (resp.) 3, 4, 5 (resp.)-almost primes whose sum of factors is a prime.

Programs

  • Mathematica
    Select[Range[8000], Last[Plus@@FactorInteger[ # ]]==6&&PrimeQ[Plus@@Times@@ Transpose[FactorInteger[ # ]]]&]
sfp6Q[n_]:=Module[{pf=Flatten[Table[#[[1]],#[[2]]]&/@FactorInteger[n]]}, Length[ pf]==6&&PrimeQ[Total[pf]]]; Select[Range[4400],sfp6Q] (* Harvey P. Dale, Jul 01 2018 *)
  • PARI
    is(n)=my(f=factor(n));sum(i=1,#f~,f[i,2])==6 && isprime(sum(i=1,#f~,f[i,1]*f[i,2])) \\ Charles R Greathouse IV, Oct 11 2013

A385968 Triprimes that are concatenations of three consecutive primes, and whose prime factors sum to a prime.

Original entry on oeis.org

199211223, 331337347, 367373379, 487491499, 653659661, 859863877, 102110311033, 106910871091, 111711231129, 112911511153, 130313071319, 143914471451, 165716631667, 178918011811, 214321532161, 226722692273, 246724732477, 274127492753, 274927532767, 284328512857, 330133073313, 362336313637
Offset: 1

Views

Author

Will Gosnell and Robert Israel, Jul 13 2025

Keywords

Examples

			a(3) = 367373379 is a term because it is the concatenation of consecutive primes 367, 373 and 379 and is the product of three primes 3 * 19 * 6445147 such that 3 + 19 + 6445147 = 6445169 is prime.

Links

Crossrefs

Intersection of A107707 and A383114.

Programs

  • Maple
    tcat:= proc(a,b,c);
  c + 10^(1+ilog10(c))*(b + 10^(1+ilog10(b))*a)
end proc:
R:= NULL: count:= 0:
q:= 2: r:= 3:
while count < 100 do
  p:= q; q:= r; r:= nextprime(r);
  x:= tcat(p,q,r);
  F:= ifactors(x)[2];
  if add(t[2],t=F) = 3 and isprime(add(t[1]*t[2],t=F)) then
     count:= count+1; R:= R,x;
  fi;
od:
R;
  • Mathematica
    tp[p_]:=FromDigits[Join[IntegerDigits/@{Prime[p],Prime[p+1],Prime[p+2]}//Flatten]];Select[Array[tp,530],PrimeOmega[#]==3&&PrimeQ[Total[First/@FactorInteger[#]]]&] (* James C. McMahon, Jul 20 2025 *)
Showing 1-4 of 4 results.

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

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