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.

A074167 Product of prime divisors of composite numbers between consecutive primes.

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%I A074167 #22 May 30 2022 02:31:11
%S A074167 1,2,6,60,6,420,6,4620,32760,30,471240,14820,42,15180,556920,15273720,
%T A074167 30,11171160,164220,6,253333080,2460,587636280,625757605200,4620,102,
%U A074167 289380,6,170940,26848135265397670224000,33540,599888520,138,39560762839197600,30
%N A074167 Product of prime divisors of composite numbers between consecutive primes.
%H A074167 Michael De Vlieger, <a href="/A074167/b074167.txt">Table of n, a(n) for n = 1..10000</a>
%F A074167 a(n) = 6 <=> A000040(n) in { A059960 }. - _Alois P. Heinz_, May 29 2022
%e A074167 a(4) = product of prime factors of composite numbers between 7 and 11 = 2 * 3 * (2 * 5) = 60.
%p A074167 a:= n-> mul(mul(i[1], i=ifactors(j)[2]), j=ithprime(n)+1..ithprime(n+1)-1):
%p A074167 seq(a(n), n=1..40);  # _Alois P. Heinz_, May 29 2022
%t A074167 Array[Times @@ Flatten@ Map[FactorInteger[#][[All, 1]] &, Range[#1 + 1, #2 - 1]] & @@ Prime[{#, # + 1}] &, 35] (* _Michael De Vlieger_, May 29 2022 *)
%o A074167 (PARI) a(n) = my(p=1); forcomposite(c=prime(n), prime(n+1), p*=factorback(factorint(c)[, 1])); p; \\ _Michel Marcus_, May 29 2022
%Y A074167 Cf. A000040, A007947, A059960, A076978.
%K A074167 nonn
%O A074167 1,2
%A A074167 _Amarnath Murthy_, Aug 30 2002
%E A074167 Corrected and extended by _Joshua Zucker_, May 08 2006
%E A074167 Offset corrected by _Alois P. Heinz_, May 29 2022