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A189982 Numbers with prime signature (2,1,1,1), i.e., factorization p*q*r*s^2 with distinct primes p, q, r, s. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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, Prime Signatures

Index to sequences related to prime signature

MATHEMATICA

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

PROG

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

CROSSREFS

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

Sequence in context: A069064 A024410 A200521 * A070237 A305416 A156687

Adjacent sequences:  A189979 A189980 A189981 * A189983 A189984 A189985

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, May 03 2011

EXTENSIONS

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

STATUS

approved

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Last modified September 17 04:58 EDT 2019. Contains 327119 sequences. (Running on oeis4.)