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Numbers of the form 5^k*p, where 1 <= k <= 5 and p is a prime different from 5.
2

%I #9 Sep 08 2022 08:45:30

%S 10,15,35,50,55,65,75,85,95,115,145,155,175,185,205,215,235,250,265,

%T 275,295,305,325,335,355,365,375,395,415,425,445,475,485,505,515,535,

%U 545,565,575,635,655,685,695,725,745,755,775,785,815,835,865,875,895,905

%N Numbers of the form 5^k*p, where 1 <= k <= 5 and p is a prime different from 5.

%C Auxiliary sequence for A128704 which gives the number of groups of order a(n).

%H Klaus Brockhaus, <a href="/A128703/b128703.txt">Table of n, a(n) for n=1..10000</a>

%e 375 = 5^3*3 is a term.

%t With[{upto=1000},Select[Union[Flatten[5^Range[5] #&/@Drop[Prime[ Range[ PrimePi[ Ceiling[upto/5]]]],{3}]]],#<=upto&]] (* _Harvey P. Dale_, Jul 27 2011 *)

%o (Magma) [ n: n in [1..910] | #t eq 2 and ((t[1, 1] lt 5 and t[1, 2] eq 1 and t[2, 1] eq 5 and t[2, 2] le 5) or (t[1, 1] eq 5 and t[1, 2] le 5 and t[2, 2] eq 1)) where t is Factorization(n) ];

%Y Cf. A128704, A000351 (powers of 5).

%K nonn

%O 1,1

%A _Klaus Brockhaus_, Mar 26 2007