A147624 Numbers n = concat(a,b) such that omega(n) = omega(a) * omega(b), where omega = A001221.

23, 25, 26, 27, 29, 32, 36, 37, 43, 46, 47, 49, 53, 56, 59, 62, 63, 65, 68, 69, 73, 76, 79, 83, 86, 89, 96, 97, 104, 108, 113, 116, 122, 123, 124, 129, 136, 137, 139, 142, 143, 144, 145, 147, 148, 152, 153, 155, 158, 159, 163, 166, 167, 169, 173, 176, 179, 183, 184

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.

Links

Table of n, a(n) for n=1..59.

Example

a(1)=23 is in the sequence since omega(23) = 1 = 1*1 = omega(2)*omega(3).
307 is not in this sequence although omega(307) = 1 = 1*1 = omega(3)*omega(07), since we don't allow leading zeros in the second part b.

Prog

(PARI) is_A147624(n)={ local(p=1, o=omega(n)); while( n>p*=10, n%p*10<p & next; o == omega( n\p )*omega( n%p ) & return(1))}
for( n=1, 999, is_A147624(n) & print1(n", "))

Crossrefs

Cf. A001221, A147616 (analog for sigma), A147619 (analog for eulerphi), A147627 (analog for bigomega).

Sequence in context: A042101 A042102 A156964 * A263315 A240913 A095251

Adjacent sequences: A147621 A147622 A147623 * A147625 A147626 A147627

Keyword

base,easy,nonn

Author

M. F. Hasler, Nov 08 2008

Status

approved