A189982 - OEIS

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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.

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: A024410 A200521 A350374 * A376374 A070237 A305416