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A067183

Numbers k such that the product of the prime factors of k equals the product of the digits of k.

1, 2, 3, 5, 6, 7, 135, 175, 735, 1176, 1715, 131712

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OFFSET

1,2

COMMENTS

Numbers k such that A007954(k) = A007947(k).

Terms are zeroless 7-smooth numbers (cf. A238985). - David A. Corneth, Sep 14 2022

LINKS

Table of n, a(n) for n=1..12.

EXAMPLE

The prime factors of 1176 are 2,3,7 which have product = 42, the product of the digits of 1176, so 1176 is a term of the sequence.

MATHEMATICA

Do[ If[ Apply[ Times, Transpose[ FactorInteger[n]] [[1]] ] == Apply[ Times, IntegerDigits[n]], Print[n]], {n, 2, 2*10^7} ]

Select[Range[2, 1000000], Times@@Transpose[FactorInteger[#]][[1]] == Times@@ IntegerDigits[#]&] (* Harvey P. Dale, Mar 19 2012 *)

PROG

(PARI) is(n) = {if(n == 1, return(1)); my(f = factor(n, 7), d = digits(n)); if(f[#f~, 1] > 7, return(0)); vecprod(f[, 1]) == vecprod(d)} \\ David A. Corneth, Sep 14 2022

CROSSREFS

Cf. A002473, A006753, A007947, A007954, A052382, A075048, A238985, A357132.

Sequence in context: A389195 A370688 A357132 * A269670 A333480 A373600

Adjacent sequences: A067180 A067181 A067182 * A067184 A067185 A067186

KEYWORD

nonn,base,fini,full

AUTHOR

Joseph L. Pe, Feb 18 2002

EXTENSIONS

Edited and extended by Robert G. Wilson v, Feb 19 2002

a(1)=1 inserted by Alois P. Heinz, Sep 14 2022

STATUS

approved

URL: https://oeis.org/A067183

⇱ A067183 - OEIS