

A147616


Numbers n = concat(a,b) such that sigma(n) = sigma(a) * sigma(b), where sigma = A000203.


4



38, 58, 66, 87, 118, 178, 205, 217, 275, 295, 298, 395, 451, 478, 492, 517, 538, 575, 660, 718, 766, 775, 838, 839, 870, 898, 1018, 1138, 1175, 1195, 1318, 1671, 1678, 1775, 1795, 1975, 2050, 2163, 2170, 2295, 2395, 2518, 2578, 2638, 2665, 2750, 2818
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OFFSET

1,1


COMMENTS

Concat(a,b) means decimal concatenation of a and b, i.e., a*10^[log[10](b)+1] + b, since we don't allow leading zeros in b. (However, allowing leading zeros in b would not give any additional term at least up to 10^6.)
This sequence has been suggested by David Wilson on the SeqFan mailing list, Nov 08 2008.
A possible variant would be to allow decomposition of n into an arbitrary number (>1) of substrings. If one requires decomposition of n into each of its digits, this yields A098771.


LINKS

Paolo P. Lava, Table of n, a(n) for n = 1..1000


EXAMPLE

a(1)=38 is in the sequence since sigma(38) = 60 = 4*15 = sigma(3)*sigma(8).


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


PROG

(PARI) is_A147616(n)={ local(p=1, s=sigma(n)); while( n>p*=10, n%p*10<p & next; s==sigma( n\p )*sigma( n%p ) & return(1))}
for(i=1, 9999, is_147616(n) & print1(n", "))


CROSSREFS

Cf. A000203, A098771, A147619 (analog for phi), A147624 (analog for omega), A147627 (analog for bigomega).
Sequence in context: A116243 A098126 A244313 * A193568 A039466 A216140
Adjacent sequences: A147613 A147614 A147615 * A147617 A147618 A147619


KEYWORD

base,easy,nonn


AUTHOR

M. F. Hasler, Nov 08 2008


EXTENSIONS

Precision about disallowed leading zeros, fix in PARI code, more cross references.  M. F. Hasler, Nov 09 2008


STATUS

approved



