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A214685 a(n) is obtained from n by removing 2s, 3s, and 5s from the prime factorization of n that do not contribute to a factor of 30. 3
1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 11, 1, 13, 7, 1, 1, 17, 1, 19, 1, 7, 11, 23, 1, 1, 13, 1, 7, 29, 30, 31, 1, 11, 17, 7, 1, 37, 19, 13, 1, 41, 7, 43, 11, 1, 23, 47, 1, 49, 1, 17, 13, 53, 1, 11, 7, 19, 29, 59, 30, 61, 31, 7, 1, 13, 11, 67, 17, 23, 7, 71, 1, 73, 37 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

In this sequence, the number 30 exhibits characteristics of a prime number.  It exhibits characteristics of a prime number since all extraneous 2s, 3s, and 5s have been removed from the prime factorizations of all of the numbers.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = (n*30^(v_30(n)))/(2^(v_2(n))*3^(v_3(n))*5^(v_5(n))), where v_k(n) is the k-adic valuation of n. That is, v_k(n) is the largest power of k, a, such that k^a divides n.

EXAMPLE

n=15, v_2(15)=0, v_3(15)=1, v_5(15)=1, v_30(15)=0, so a(15) = 30^0*15/(2^0*3^1*5^1) = 1.

n=60, v_2(60)=2, v_3(60)=1, v_5(60)=1, v_30(60)=1, so a(60) = 30^1*60/(2^2*3^1*5^1) = 30.

MAPLE

a:= proc(n) local i, m, r; m:=n;

      for i from 0 while irem(m, 30, 'r')=0 do m:=r od;

      while irem(m, 2, 'r')=0 do m:=r od;

      while irem(m, 3, 'r')=0 do m:=r od;

      while irem(m, 5, 'r')=0 do m:=r od;

      m*30^i

    end:

seq(a(n), n=1..100);  # Alois P. Heinz, Jul 04 2013

PROG

(Sage)

n=100 #change n for more terms

C=[]

b=30

P = factor(b)

for i in [1..n]:

....prod = 1

....for j in range(len(P)):

........prod = prod * ((P[j][0])^(Integer(i).valuation(P[j][0])))

....C.append((b^(Integer(i).valuation(b)) * i) /prod)

CROSSREFS

Cf. A214681, A214682.

Sequence in context: A318674 A284118 A165725 * A327670 A178637 A295294

Adjacent sequences:  A214682 A214683 A214684 * A214686 A214687 A214688

KEYWORD

easy,nonn

AUTHOR

Daniel Juda, Jul 25 2012

STATUS

approved

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Last modified November 16 17:25 EST 2019. Contains 329201 sequences. (Running on oeis4.)