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

1,2

Links

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

Formula

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

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A114925 A043270 A089898 * A351868 A325721 A079050

Adjacent sequences: A071782 A071783 A071784 * A071786 A071787 A071788

Keyword

nonn,base,mult

Author

Reinhard Zumkeller, Jun 06 2002

Status

approved