cp's OEIS Frontend

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

%I A071785 #16 Oct 22 2021 12:19:43
%S A071785 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,
%T A071785 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,
%U A071785 54,10,56,30,22,14,60,7,8,63,64,20,12,13,32,15,70,8,72
%N A071785 In prime factorization of n replace each prime with the sum of its decimal digits.
%H A071785 Rémy Sigrist, <a href="/A071785/b071785.txt">Table of n, a(n) for n = 1..10000</a>
%F A071785 Multiplicative with a(p) = A007953(p), p prime.
%F A071785 a(n) = n iff n is 7-smooth (A002473).
%e A071785 a(143) = a(11*13) = a(11)*a(13) = (1+1)*(1+3) = 2*4 = 8.
%p A071785 a:= n-> mul(add(j, j=convert(i[1], base, 10))^i[2], i=ifactors(n)[2]):
%p A071785 seq(a(n), n=1..72);  # _Alois P. Heinz_, Oct 22 2021
%t A071785 a[n_] := Product[{p, e} = pe; Total[IntegerDigits[p]]^e, {pe, FactorInteger[n]}];
%t A071785 Table[a[n], {n, 1, 100}] (* _Jean-François Alcover_, Oct 22 2021 *)
%o A071785 (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
%Y A071785 Cf. A002473 (fixed points), A007953, A072084 (binary variant).
%K A071785 nonn,base,mult
%O A071785 1,2
%A A071785 _Reinhard Zumkeller_, Jun 06 2002