A189982 Numbers with prime signature (2,1,1,1), i.e., factorization p*q*r*s^2 with distinct primes p, q, r, s.

420, 630, 660, 780, 924, 990, 1020, 1050, 1092, 1140, 1170, 1380, 1386, 1428, 1470, 1530, 1540, 1596, 1638, 1650, 1710, 1716, 1740, 1820, 1860, 1932, 1950, 2070, 2142, 2220, 2244, 2380, 2394, 2436, 2460, 2508, 2550, 2574, 2580, 2604, 2610, 2652, 2660, 2790

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, May 03 2011

Keywords

• nonn

Comments

Theorem 4 in Goldston-Graham-Pintz-Yildirim proves that a(n+1) = a(n) + 1 for infinitely many n. - Charles R Greathouse IV, Jul 17 2015, corrected by M. F. Hasler, Jul 17 2019

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• D. A. Goldston, S. W. Graham, J. Pintz, and C. Y. Yıldırım, Small gaps between almost primes, the parity problem, and some conjectures of Erdos on consecutive integers (2008)
• Will Nicholes, List of Prime Signatures
• Index to sequences related to prime signature

Crossrefs

Part of the list A178739 .. A179696 and A030514 .. A030629, A189975 .. A189990 etc., cf. A101296.

Programs

Mathematica

f[n_]:=Sort[Last/@FactorInteger[n]]=={1,1,1,2}; Select[Range[4000],f]

PARI

is(n)=vecsort(factor(n)[,2])==[1, 1, 1, 2]~ \\ Charles R Greathouse IV, Jul 17 2015

Extensions

Definition reworded by M. F. Hasler, Jul 17 2019