OFFSET

1,1

COMMENTS

Concat(a,b) means decimal concatenation of a and b, i.e., a*10^floor(log_10(b)+1) + b, since we do not allow leading zeros in b. However, allowing for leading zeros in b would not give any additional term below 10^6.

This sequence was suggested by Farideh Firoozbakht and David Wilson on the SeqFan mailing list, Oct 27 and Nov 06 2008 (see Links).

Farideh Firoozbakht has proved that if n is in this sequence, then n*10 is again in the sequence. Thus one could call "primitive" terms of this sequence those which aren't multiples of 10.

A possible variant would be to allow decomposition of n into an arbitrary number of substrings. If one requires decomposition of n into each of its digits, i.e., the analog of A098771 with sigma replaced by phi, then 78 appears to be the only number having this property.

LINKS

Paolo P. Lava, Table of n, a(n) for n = 1..500

David Wilson, A nice (decimal) property of 78, Seqfan mailing list (Nov 2008).

MAPLE

with(numtheory): P:=proc(q) local s, t, k, n; for n from 1 to q do

for k from 1 to ilog10(n) do s:=n mod 10^k; t:=trunc(n/10^k);

if s*t>0 then if phi(s)*phi(t)=phi(n)

then print(n); break; fi; fi; od; od; end: P(10^5); # Paolo P. Lava, Jan 27 2015

PROG

(PARI) is_A147619(n)={ local(p=1, s=eulerphi(n)); while( n>p*=10, n%p*10<p & next; s==eulerphi( n\p )*eulerphi( n%p ) & return(1))}

for( n=1, 10^5, is_147619(n) & print1(n", "))

CROSSREFS

KEYWORD

base,easy,nonn

AUTHOR

M. F. Hasler, Nov 08 2008

STATUS

approved