A270142 a(n) = product of first k composites, with the i-th composite raised to the d-th power, where k = A055642(n) and d is the i-th digit of n.

4, 16, 64, 256, 1024, 4096, 16384, 65536, 262144, 4, 24, 144, 864, 5184, 31104, 186624, 1119744, 6718464, 40310784, 16, 96, 576, 3456, 20736, 124416, 746496, 4478976, 26873856, 161243136, 64, 384, 2304, 13824, 82944, 497664, 2985984, 17915904, 107495424

Offset

1,1

Comments

All terms are multiples of 4, since A002808(1) = 4 and the most significant digit of n is always nonzero.

Does a term exist such that a(n) = n? Such a number would be the analog of a Meertens number when raising composites to the powers of the digits of n instead of raising primes to the powers of the digits.

From Chai Wah Wu, Dec 15 2022: (Start)

If a(n) is defined using digits of n in base b, then there are bases b and numbers n such that a(n) = n. For instance:

base b n

------------------------------------------------

2 4, 24, 36, 24192000, 85155840

3 2592

4 4, 103680

6 20736

8 16, 256, 13824

12 1327104

16 21233664

23 24

24 746496

(End)

Links

Felix Fröhlich, Table of n, a(n) for n = 1..10000

Example

a(12) = 144, since A002808(1) = 4, A002808(2) = 6 and 4^1 * 6^2 = 144.

Prog

(PARI) composite(n) = my(i=0, c=2); while(1, if(!ispseudoprime(c), i++); if(i==n, return(c)); c++)
compopowerprod(n) = my(d=digits(n)); for(k=1, #d, p=prod(i=1, #d, composite(i)^d[i])); p
a(n) = compopowerprod(n)
(Python)
from math import prod
from sympy import composite
def A270142(n): return prod(composite(i)**int(d) for i, d in enumerate(str(n), 1)) # Chai Wah Wu, Dec 09 2022

Crossrefs

Cf. A189398, A246532.

Sequence in context: A215877 A206450 A294452 * A000302 A262710 A050734

Adjacent sequences: A270139 A270140 A270141 * A270143 A270144 A270145

Keyword

nonn,base,easy

Author

Felix Fröhlich, Mar 12 2016

Status

approved