A258885 Primitive weird numbers (A002975) having 6 distinct prime factors.

1550860550, 44257207676, 66072609790

Offset: 1

Author

Douglas E. Iannucci and Robert G. Wilson v, Jun 14 2015

Keywords

• nonn
• bref
• hard
• more

Comments

a(4) <= 5976833582079328 = 2^5*181*197*353*431*34429 and a(5) <= 48083019473926272314825065088 = 2^7*257*97213*97973*100957*1520132521 that is certainly in this sequence. - Giuseppe Melfi, Oct 26 2015

a(4) <= 125258675788784 = 2^4 * 47 * 149 * 353 * 1307 * 2423. - M. F. Hasler, Jul 12 2016

Examples

			a(1) = 1550860550 = 2 * 5^2 * 29 * 37 * 137 * 211 = A273815(1). (Abundance = 20)
a(2) = 44257207676 = 2^2 * 11 * 37 * 59 * 523 * 881. (Abundance = 8, cf. A088833)
a(3) = 66072609790 = 2 * 5 * 11 * 127^2 * 167 * 223 = A273815(3). (Abundance = 4, cf. A088832)
		

Links

• G. Amato, M. F. Hasler, G. Melfi and M. Parton, Primitive weird numbers having more than three distinct prime factors, Riv. Mat. Univ. Parma, Vol. 7, No. 1 (2016) 153-163.
• G. Melfi, On the conditional infiniteness of primitive weird numbers, Journal of Number Theory, 147 (2015) 508-514; Lemma 2.

Crossrefs

Cf. A002975, A258401, A258882, A258883, A258884.

Programs

Mathematica

(* copy the terms from A002975, assign them to 'lst' and then *)
Select[ lst, PrimeNu@# == 6 &]

PARI

select(w->omega(w)==6, A002975) \\ Assuming that A002975 is defined as set or vector. - M. F. Hasler, Jul 12 2016

Extensions

One more term added and definition corrected by Giuseppe Melfi, Nov 02 2015