A071785 In prime factorization of n replace each prime with the sum of its decimal digits.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 12, 4, 14, 15, 16, 8, 18, 10, 20, 21, 4, 5, 24, 25, 8, 27, 28, 11, 30, 4, 32, 6, 16, 35, 36, 10, 20, 12, 40, 5, 42, 7, 8, 45, 10, 11, 48, 49, 50, 24, 16, 8, 54, 10, 56, 30, 22, 14, 60, 7, 8, 63, 64, 20, 12, 13, 32, 15, 70, 8, 72

Offset: 1

Author

Reinhard Zumkeller, Jun 06 2002

Keywords

• nonn
• base
• mult

Examples

			a(143) = a(11*13) = a(11)*a(13) = (1+1)*(1+3) = 2*4 = 8.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002473 (fixed points), A007953, A072084 (binary variant).

Programs

Maple

a:= n-> mul(add(j, j=convert(i[1], base, 10))^i[2], i=ifactors(n)[2]):
seq(a(n), n=1..72);  # Alois P. Heinz, Oct 22 2021

Mathematica

a[n_] := Product[{p, e} = pe; Total[IntegerDigits[p]]^e, {pe, FactorInteger[n]}];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Oct 22 2021 *)

PARI

a(n, base=10) = my (f=factor(n)); prod(i=1, #f~, sumdigits(f[i,1], base)^f[i,2]) \\ Rémy Sigrist, Feb 19 2019

Formula

Multiplicative with a(p) = A007953(p), p prime.

a(n) = n iff n is 7-smooth (A002473).