A100753 Numbers which can be obtained as the product of one or more of their digits (used with multiplicity).

1, 2, 3, 4, 5, 6, 7, 8, 9, 25, 32, 36, 64, 125, 128, 135, 175, 216, 243, 250, 256, 324, 375, 384, 432, 512, 625, 672, 729, 735, 784, 864, 875, 1024, 1250, 1296, 1372, 1715, 1764, 1792, 2048, 2304, 2500, 2560, 2592, 2744, 2916, 3072, 3087, 3125, 3375, 3456, 3645

Offset

1,2

Comments

Subsequence of the 7-smooth numbers (A002473).

For 2 <= d <=9, powers of d that contain digit d are in the sequence, e.g. every power of 5 and every odd power of 9.

Links

Table of n, a(n) for n=1..53.

Example

64 is a member as 64 = 4*4*4; 135 is a member as 135 = 3*3*3*5.

Prog

(PARI) digits29(n) = local(v, d); v=[]; while(n>0, d=divrem(n, 10); n=d[1]; if(d[2]>1, v=concat(d[2], v))); v {recdiv(n, s) = local(b, j, d); b=0; j=1; while(b<1&&j<=length(s), d=divrem(n, s[j]); if(d[2]==0, if(d[1]>1, b=recdiv(d[1], s), b=1)); j++); b} for(n=1, 3650, if(n==1||recdiv(n, digits29(n)), print1(n, ", ")))

Crossrefs

Cf. A002473.

Sequence in context: A095706 A280249 A096867 * A359494 A132416 A128606

Adjacent sequences: A100750 A100751 A100752 * A100754 A100755 A100756

Keyword

base,easy,nonn

Author

Amarnath Murthy, Nov 22 2004

Extensions

Edited, corrected and extended by Klaus Brockhaus, Nov 25 2004

Status

approved