A319352 -id:A319352 - cp's OEIS frontend

A319353 Filter sequence combining weights of partitions with Heinz-numbers equal to the proper divisors of n.

1, 2, 2, 3, 2, 4, 2, 4, 5, 6, 2, 7, 2, 8, 9, 10, 2, 11, 2, 11, 12, 13, 2, 14, 15, 16, 12, 17, 2, 18, 2, 11, 19, 20, 21, 22, 2, 23, 24, 18, 2, 25, 2, 26, 27, 28, 2, 29, 30, 31, 32, 33, 2, 25, 34, 25, 35, 36, 2, 37, 2, 38, 39, 40, 41, 42, 2, 43, 44, 45, 2, 37, 2, 46, 47, 48, 49, 50, 2, 51, 52, 53, 2, 54, 55, 56, 57, 42, 2, 58, 59, 60, 61, 62, 63, 37, 2, 64, 65

Offset: 1

Antti Karttunen, Sep 17 2018

nonn

Restricted growth sequence transform of A319352.
For all i, j:
  a(i) = a(j) => A301855(i) = A301855(j).
  a(i) = a(j) => A304793(i) = A304793(j).

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A056239, A319352.

up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i,2] * primepi(f[i,1]))); }
A319352(n) = { my(m=1); fordiv(n, d, if(dA056239(d)))); (m); };
v319353 = rgs_transform(vector(up_to,n,A319352(n)));
A319353(n) = v319353[n];

A319692 a(n) = Product_{d|n, dA001414(d)), where A001414(d) gives the sum of prime factors of d, with repetition.

Original entry on oeis.org

1, 2, 2, 10, 2, 70, 2, 110, 14, 130, 2, 10010, 2, 190, 182, 1870, 2, 15470, 2, 27170, 266, 370, 2, 3233230, 26, 430, 238, 60610, 2, 5169710, 2, 43010, 518, 610, 494, 74364290, 2, 710, 602, 13394810, 2, 15543710, 2, 175010, 71162, 890, 2, 2156564410, 38, 76570, 854, 250690, 2, 10318490, 962, 38123690, 994, 1130, 2, 971341981610, 2, 1310, 140182, 1333310, 1118

Offset: 1

Antti Karttunen, Oct 02 2018

nonn

Antti Karttunen, Table of n, a(n) for n = 1..8192

Cf. A001414, A319693 (rgs-transform).

Cf. also A319352.

A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.
A319692(n) = { my(m=1); fordiv(n, d, if(dA001414(d)))); (m); }; \\ Antti Karttunen, Oct 02 2018

a(n) = Product_{d|n, dA000040(1+A001414(d)).
For all n >= 1:
A001221(a(n)) = A305611(n).

cp's OEIS Frontend

A319353 Filter sequence combining weights of partitions with Heinz-numbers equal to the proper divisors of n.

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